Barcelona's fans are heading down the Ramblas again, gathering round the Canaletas fountain and packing the city's famous tree-lined avenue. This is getting silly now. May has seemed like an almost continuous party, momentarily cleared in the morning for traders to set up stalls selling flowers, tarantulas and budgies in cages, only to be cranked up again as darkness falls.

Tonight was the fifth time they have been there, letting off fireworks, dancing, drinking and singing, in the past month alone. They were there on 2 May to celebrate their team hammering Real Madrid 6-2 at the Santiago Bernabéu; they were there four nights later when Andrés Iniesta scored a late equaliser against Chelsea to send them to the Champions League final; and, with their team 3-1 up, some of them were even prematurely there four days after that to celebrate a league title that was denied by Joseba Llorente's 90th minute equaliser for Villarreal.

That was but a temporary blip – they were there three days after that to celebrate winning the Copa del Rey against Athletic Bilbao and they were there again three days after that when Madrid's defeat at Villarreal mathematically crowned them champions. This though was the biggest victory of all and will be the biggest party too. Not just because it is their greatest achievement – Barcelona have won 24 cups and 18 leagues before, yet only three European Cups – but because of everything it represents.

This is a celebration not just of the European Cup but an extraordinary season, a historic one. Victory in Rome made it so. It was already special, Barcelona won the league in stunning style, their Bernabéu victory was the biggest in their history and with a week left, they have already scored 104 goals. (If they don't break Madrid's record of 107 this weekend, it's because they were too good to break it: playing reserve teams, they've lost their last two scoring just once).

Yet something was missing. Tonight, it was delivered. A European Cup. Victory against the holders, English holders. The side that Pep Guardiola declared the world's best reduced to chasing after the ball in vain.

In the build-up to the final Guardiola was asked if, in a roundabout sort of way, it didn't matter if Barcelona lost. "Of course it matters," he replied. "We have to think it's absolutely fundamental to win. It's Manchester United, the best team in the world. If you go there thinking, 'It's no big deal', then there's a 100% chance of losing. Yes, we've had a great season but we want to show the world how we've been playing."

Tonight showed that this Barcelona genuinely is a phenomenal side, maybe the best they've ever had. All season two words have been inescapable: "Dream" and "Team". A legend as a player, Johann Cruyff's return as coach changed the club when he led the Dream Team to four successive leagues between 1991 and 1994 and their first ever European Cup with an unshakeable commitment to a technical approach. Every team since has been measured against that team - a mythical image of perfection – and every team since has failed to live up to it. Until now.

Barcelona suffered their worst ever start to a season but by clinching the European Cup in his first year – Cruyff took four – Guardiola has given Barcelona their best ever end. This is their first treble, the first won by a Spanish club. Only four clubs in Europe have matched that feat: Celtic, Ajax, PSV, and of course United.

Nor is it just about substance, it is about style too. Barcelona have done it playing wonderful football, inspired by Cruyff, faithful to his legacy. Virtually all season, this side has been heralded as the new Dream Team. Josep Lluís Núñez, the president during that era, declared Guardiola's side better than Cruyff's. And all season long it has appeared premature, maybe even faintly ludicrous. Right now, as the Ramblas hosts yet another party, it is justified.