Leeds United's players marked the appointment of Neil Warnock as the club's new manager with a stirring comeback from two goals down to beat Doncaster 3-2 in the Championship.

Warnock, who watched the match from the stands at Elland Road but addressed the players before the game and at half-time, was named as the replacement for Simon Grayson early on Saturday. He pledged to mastermind a quick return to the Premier League – both for Leeds and for himself, after his sacking by Queens Park Rangers last month.

Warnock, who met the Leeds chairman Ken Bates in Monaco during the week to discuss his 18-month contract, said: "I feel I have one big challenge left in me and believe Leeds is a club that should be in the Premier League. I want to be the man who is able to deliver this for a set of fans who never cease to amaze me with their numbers and their loyalty.

"Having met with Ken it was an easy decision to take up the challenge and, with his support, we share the same vision of getting Leeds United in the Premier League."

Saturday's three points took Leeds to 10th in the Championship and just three points off the play-offs, and Bates pledged to provide the financial backing for Warnock to take the club on.

Bates said: "We want to be in the Premier League and we will support Neil in the quest to get us there. We believe the appointment is arguably the most important we have made. The objective was to appoint a manager who had a proven track record of getting teams promoted and, in Neil, we have a man whose record is second to none."

Before winning the Championship last season with QPR, Warnock had previously led Sheffield United and Notts County to promotion to the top flight.

Leeds confirmed the 63-year-old will be able to appoint his own backroom staff. Neil Redfearn, who had been placed in temporary charge after Grayson's departure, was in the dugout for the win over Doncaster, but is now set to return to his role with the Leeds academy.

Warnock, often as controversial a figure as his new chairman, was welcomed by the head of the Leeds' supporters' club. Ray Fell told Sky: "He's a man who can motivate us and reopen our season. He'll give us experience and get the most out of the players, which for the last period hasn't been happening."

Writing in his Saturday newspaper column before his appointment was announced, Warnock hinted that Leeds would be the 13th club of his 32-year managerial career by stating there were "possibilities cropping up that may offer the chance to get back into the game" including "one of the top six clubs in England in Leeds."

He made clear that managing below the Premier League would be no problem. "If I do take a job it's got to be at a club that gets me excited and gets the hairs on the back of my neck to stand up. That's the type of job that keeps me going and all three I have mentioned fit that bill.

"It doesn't really bother me which division I manage in – I'm not one to say I have to be in the Premier League. There are plenty of good clubs outside it."

Leeds's dismal first-half performance against Doncaster may have been what prompted Warnock's unexpected half-time intervention, but his words initially seemed to have had little effect, Mamadou Bagayoko quickly following up his first-half opener with a second after the break.

That prompted another outpouring of dissent from the stands, with Leeds's fans renewing their attacks on Bates over a perceived lack of investment. Doncaster's fans, meanwhile – no friends of Warnock after his long stint in charge of their local rivals Sheffield United – joined in, taunting him from their position next to the directors' box.

However Leeds turned it around. A minute after Bagayoko's second, Luciano Becchio fumbled his way into the box, the ball fell to Andros Townsend and he placed a crisp drive beyond David Button. Becchio then drew a low save out of Button, after Robert Snodgrass's cross, before the keeper saved at the feet of Ross McCormack.

The momentum was now all with Leeds and when they equalised with 10 minutes remaining it had been coming. Snodgrass fizzed a cross in from the left and Adam Clayton arrived in the box to stab the ball beyond Button on the volley. But that was not the end of the drama. After a lengthy delay after an injury to Robbie Rogers, Becchio curled in a dramatic 20-yard winner.

Redfearn said Warnock had made an impression in the dressing room. "Neil had a big impact. He came in at half-time and made a few points. It was sensible advice in the situation we were in.

"He said they should be a bit more positive, with more energy, and play higher up the pitch. There was no ranting and raving. Our second-half performance was more like it. We got about them and the crowd responded."

Redfearn, who took over when Simon Grayson was sacked, said: "The appointment of Neil Warnock is fantastic for the club. He has a track record of getting teams out of this division and these are exciting times."

The defeat leaves Doncaster bottom, having failed to win any of their last five league games and none in eight away from home. They have taken only one away point since a 3-2 victory at Ipswich on 5 November.