"Madrid is red and white" said Diego Simeone and Madrid was red and white. Outside the Vicente Calderón, up the Paseo de los Melancólicos, along Pontones and Acacias, around Ortega y Munilla and over Embajadores, it was red and white. In the middle, the bus was blue. Spain's new champions were on board and for the first time in a decade they were not from Real Madrid or FC Barcelona. Up the Ronda de Valencia, across the Plaza del Emperador Carlos V, Reina Sofia art gallery to the right, Atocha station to the left and on to the Paseo del Prado. At the end, four kilometres from where they had set off, Neptune waited. Thousands more supporters waited too.

Atlético's players, league champions 18 years later, started arriving at the stadium at seven. Mostly they came in flash cars, triumphantly revving engines as they roared into the garage, but David Villa, Raúl García and captain Gabi came in a van, hanging out of the top and the side. There, they boarded the bus, a slogan painted on the back: "History is written heartbeat by heartbeat." There was no trophy on show. The president of the Football Federation was busy "travelling", apparently. "It doesn't matter: they can't take it off us," Simeone said, summing it up: Spanish football saves itself from those who preside over it.

No one cared. The bus made slow, stuttering progress. Fans lined the way. They waved from balconies, climbed trees and clambered up traffic lights. Others followed, running alongside blowing kisses like sweethearts watching a train pulling out the station. Red and white mopeds and bicycles provided a cavalcade. A line of taxis was halted all the way down Méndez Álvaro, doors open, drivers and passengers outside, watching. Flares lit them up, from down below and from on deck. At Neptune, it was packed. Up past parliament, you could see no street. Down past the Ministry of Health you couldn't either. Or the other way, towards Cibeles; 200,000 people were out, some reports said. Or more.

A police cordon created an island in the middle of the square where Neptune stands, trident in hand. As the players paraded on the platform, presented to the crowd one by one, as Gabi climbed on to Neptune, behind the scaffolding Simeone's dad stood quietly, proudly. This was different, he said. This was something more. Up on the stage, his son took the microphone. "This is not just a league," Simeone said, "what this triumph transmits is much more important than that. If you believe and if you work, you can do it."

It was a familiar message. Atlético midfielder Tiago has described them as "Football's Robin Hood" and the manager has made much of their identification with the people in times of crisis, keen to insist on "sacrifice" and hard work, to those who fight to survive daily. Game by game, day by day. To some extent, it is a cliché but it has been turned into a philosophy. Cholismo, it has been called. And it has turned out to be true. Atlético had actually done it.

They shouldn't have been able to. It is forgotten now in the rush to insist that everyone else wrote them off, but Simeone said winning this league was "impossible." When Atlético lost at Espanyol, he almost seemed pleased. "You'll see I was right," he said, it would be Madrid and Barcelona at the top at the end of the season. But it is not. That he was right to say so makes this an even more astonishing achievement. It may have been heard before but it is worth saying again. However you look at this, it is barely believable.

No one outside of Madrid or Barcelona has won the league in a decade. Atlético went to the Santiago Bernabéu and took the Copa del Rey off Real Madrid. Exactly a year later, they went to the Camp Nou and took the league off Barcelona. On Saturday they go to Lisbon. It is the first time they have been in a European Cup final for 40 years. This is their first league title for 18 years. They had not even been top, not even for a single week, in 16 years until this season. They had waited 14 years and 25 games to beat Real Madrid and the next time they played them they won again.

They had wanted Simeone to come from the day he had departed after the second time as a player; he had wanted to as well. Here was someone who could unite the club, utterly identified with it. All of it except that losing complex. Simeone won the double with Atlético as a player in 1996. The sporting director, José Luis Caminero, was in that team too. So was Juan Vizcaíno, now on Simeone's staff. As is the Germán 'El Mono' Burgos; it was Burgos who appeared in an advert for Atlético, emerging from the sewers to warn that they were coming back after relegation in 1999, those two little years in "hell". Simeone made them join him in the post match press conference at the Camp Nou in a gesture that spoke volumes. "They don't appear on the television but I want you to know how much I admire them," he said.

But no one expected this. Has a manager ever had such an immediate and profound impact? When Simeone took over two days before Christmas 2011, Atlético were 10th and had just been defeated by Second Division B side Albacete in the Copa del Rey. They were "sunk", the captain says. These are the same players. His character has transformed them; as has his work. They finished fifth and won the Europa League, following that up with a European Super Cup demolition of Chelsea. Then they reached the Champions League places and won the Copa del Rey. Now they have won an impossible league and have reached the European Cup final. They have won more than their city rivals in that time; more than Barcelona too.

Atlético have played Barcelona six times this season and not lost. They took the title from Barcelona at the Camp Nou. They won at the Bernabéu, at San Mamés, at Anoeta, at the Sánchez Pizjuán and at Mestalla. They also won at San Siro and at Stamford Bridge, of course. They did not lose a game at home. This was no fluke.

It is impossible to judge, but this may have been the hardest Spanish league title to win. Yes, ever. Logic suggested that a decade of dominance would be extended. As Simeone put it, there is "only a €400m difference" between their budget and that of the big two; each year Madrid and Barcelona take three times more in TV money alone. Atlético's income is still embargoed by the tax man; this is no model club. In the summer, Atlético's top scorer left. This summer, Atlético's new top scorer will leave too. When the final whistle went on Saturday night and Atlético won the league, the 11 players on the pitch had cost under €40m. Less than Cesc Fábregas. Or Asier Illarramendi.

They had done it the hard way. As the season headed into the final weeks, they appeared exhausted. They had reached a final, two semi-finals and had played the Spanish Super Cup, losing it on away goals, unbeaten. Rarely had they rotated; rarely could they. The full back Filipe Luís talked about a pressure that was brutal.

They had long thought that fixtures may favour them; on the final day Barcelona would either be out of it or would prefer them to take the title than Madrid. And besides Atlético had been a fraction away from being champions before they even got to Barcelona. Adrian's shot in the 94th minute of the penultimate week would have meant taking the league, but it was pushed away by Málaga goalkeeper Willy Caballero. Instead, the draw and Real Madrid's loss meant Barcelona had no doubts and had their destiny in their own hands and at home: win and they would win the league; Atlético would be denied.

Atlético had looked shattered when the final whistle went on the Málaga game. And then, six days later, it got worse. On the touchline at the Camp Nou, Simeone stood shaking his head sadly, biting his lip. This was too cruel to contemplate. Diego Costa was off in tears; Arda Turan was off in tears. Then Alexis Sánchez scored an implausibly brilliant goal out of nothing that screeched into the net. Tata Martino's face said it all: a relieved, conspiratorial look that said bloody hell, that was lucky: let's sneak off with it now, before anyone notices.

At half time, a priest took a photograph of an Atlético fan who had turned up at his church to pray. . At the same time, Simeone was telling his players they were the better team. Three chances came in the first three minutes of the second half. One post, one saving tackle, one goal. Diego Godín scored. It was the 13th goal Atlético had scored from a dead ball – more than anyone else. There was a long way to go but, Leo Messi's disallowed goal aside, Barcelona created nothing. Atlético would not let them. When the whistle went, Simeone was almost knocked over in the stampede. He put his head in his hands and turned towards the bench quietly, slowly. Then Mono Burgos tapped him on the back. They screamed and embraced, a great big bear hug from a great big bear of a man.

Simeone sat on the bench, an almost maniacal smile of disbelief stretching across his face, like a master criminal whose diabolical plan had worked to perfection. Then he pulled out his phone and rang his children in Argentina. Gabi was lying on the turf, head down, sobbing. All around the ground there was applause. At the final whistle, the Camp Nou had immediately broken into an ovation. There were even some chants of "Atléti!". Although it hurt, they knew that they had witnessed something extraordinary, something that was impossible not to admire.

High on the top of the stand opposite were 20 flags, one for each team in the league. They were arranged in order of the league table. Atlético Madrid's had been run up the first flag pole, red and white. No one will be taking it down now.

Talking points

• And at the bottom ...

On the final day of the season, with five teams trying to avoid the last two relegation places, there were thirty-three minutes of injury time played. Fortunately, the injuries were only minor. It all began when Osasuna scored the opening goal against Betis. Fans in the front row, many of whom were perched on the metal barriers at he front of the stand, started celebrating and the pressure build from behind them. The barrier gave way and they fell to the ground, two or three metres below. Players and staff from both teams rushed over, with Betis midfielder Alfred N'Diaye among those helping to carry fans away. Physiotherapists and doctors from the teams joined with Red Cross staff to attend to them. In the end, there were 68 fans injured, 10 of whom were taken to hospital. Fortunately, none were seriously hurt.

The game was stopped for 35 minutes. Discussions were held with the players and club staff; the captains spoke to the supporters involved. Because of the drop in front of the stand, the seats could not be reoccupied. So, the front rows were vacated and supporters stood pitchside behind the advertising boards with a cordon of security in front of them instead.

While the Osasuna game stopped, the other relegation games were going on. The league decided that they had to be held simultaneously, so when the other matches reached half time, the teams waited and did not go out for the second half until Osasuna and Betis were able to do the same. Because Osasuna and Betis still had 33 minutes of the first half left, that essentially meant that Osasuna-Betis had a ten minute half time and that Almería-Athletic, Rayo-Getafe, and Valladolid-Granada all had a 45 minute half time break. It also meant that the games did not finish until 8.17pm.

The drama on the pitch was limited. Although Getafe did not get the winner in Vallecas until the 92nd minute and although there were confrontations between the two managers (and, according to reports in Marca, between Rayo's players at half time, with some suspecting others of not trying), that late goal did not change anything. Almería got the draw they needed just in case, Osasuna were leading early but always knew their fate was in the hands of others and in the direct clash Granada were leading Valladolid from the 43rd minute. At the start of the day, Osasuna and Valladolid were in the relegation zone and they ended it there too.

"The silence in the dressing room is sepulchral," said Valladolid manager Juan Ignacio Martínez afterwards. In Pamplona, where Osasuna went down after fourteen years in which they have consistently made life difficult for the big clubs, it was a particularly cruel end for Patxi Puñal. The club captain, who began his career by cycling to training from the factory where he worked, was playing his last game after a seventeen-season career. "My career has been hard, but I never imagined that the hardest moment would be saved until last," Puñal said. "I am proud of these fans and I wish I could have said goodbye in better circumstances."

At Almería, where they celebrated survival by throwing their boots into the crowd last week only to realise that they weren't actually safe yet and have to appeal to get the boots back, there were ultimately few worries, thanks to an amazing run in the last month. The team with the youngest manager in the top flight will be back next year.

One man who won't be back for Almería is goalkeeper Esteban. The thirty eight year old reckons he has missed just two training sessions in a twenty year career. He is not retiring but he is leaving, despite being ever-present this season and being the goalkeeper with the second most saves in the division, despite being more than good enough to continue. Instead, he is dropping down to the Second Division B to play for the team where he started his professional career and the club he supported as a kid: Real Oviedo. "I have a friend who I thought I could help," he said.

Results: Málaga 1-0 Levante, Real Madrid 3-1 Espanyol, Barcelona 1-1 Atlético, Valencia 2-1 Celta, Real Sociedad 1-2 Villarreal, Rayo 1-2 Getafe, Almería 0-0 Athletic, Valladolid 0-1 Granada, Osasuna 2-1 Betis, Sevilla 3-1 Elche.

Champions: Atlético

Champions League places: Barcelona, Real Madrid, Athletic.

Europa League places: Sevilla, Villarreal, Real Sociedad.

Relegated: Betis, Valladolid, Osasuna.

Cup winners: Real Madrid.

Pichichi: Cristiano Ronaldo, 31.

Zamora: Thibaut Courtois.

Fond farewell: Retirees Carles Puyol, Patxi Puñal.

Coaches waving goodbye (so far): Tata Martino, Luis Enrique, Paco Jémez (he says), Juan Ignacio Martínez, Bernd Schuster, Javier Aguirre, and Lucas Alcaraz, who said: "I'm like a taxi: I'll put my 'free' sign up and see if anyone hails me".

Final La Liga standings