On Wednesday, the 24-year-old striker said concerns over the strength of the club's squad were behind his original decision not to sign a new deal.
United boss Sir Alex Ferguson said: "I'm delighted Wayne's agreed to stay."
Rooney stated: "I said on Wednesday the manager's a genius and it's his belief and support that convinced me to stay."
The England international, who will be out for three weeks after injuring his ankle during training on Tuesday, added: "I'm delighted to sign another deal at United. I've spoken to the manager and the owners and they've convinced me this is where I belong.
"I am signing a new deal in the absolute belief that the management, coaching staff, board and owners are totally committed to making sure United maintains its proud winning history - which is the reason I joined the club in the first place.
"I am sure the fans over the last week have felt let down by what they have read and seen.
"But my position was from concern over the future.
"The fans have been brilliant with me since I arrived and it's up to me through my performances to win them over again."
The agreement ends a period of intensive discussions at Old Trafford after Rooney issued a statement in which he revealed that United chief David Gill had not given him the assurance he was seeking about the future squad.
"It's been a difficult week but the intensity of the coverage is what we expect at Manchester United," Ferguson told the club's website.
"Sometimes, when you're in a club, it can be hard to realise just how big it is and it takes something like the events of the last few days to make you understand.
"I think Wayne now understands what a great club Manchester United is.
"I'm pleased he has accepted the challenge to guide the younger players and establish himself as one of United's great players.
"It shows character and belief in what we stand for.
"I'm sure everyone involved with the club will now get behind Wayne and show him the support he needs to produce the performances we know he is capable of."
Rooney's team-mate Rio Ferdinand said on social networking website Twitter: "It was never in doubt in my mind tweeps, Wazza is Man Utd through and through there's no way I could have seen him playing for another club, defo not a Prem club anyway."
Former United midfielder Lou Macari admitted that he was surprised by the news.
He told BBC Radio 5 live: "I didn't see this coming.
"It's going to be difficult for Wayne to get everyone back on board. I don't think it will be as easy as just scoring goals. It's going to take a lot of other things and over a period of time he'll learn to get back on with his football."
United supporter Liam Bradford, who is the assistant editor of the Red News fanzine also told Radio 5 live: "I'm completely flabbergasted.
"It's been one of those weeks. It's been completely mad.
"I don't know whether this has been planned all along and this was just some elaborate mind game that Sir Alex Ferguson was playing with Wayne Rooney on board or whether it has just been completely surreal for the last seven days.
"At the end of the day, he is a world-class footballer and I really wouldn't want to see him anywhere else. I think I'm more relieved that anything he is not going across the city to the team that plays in blue."
Rooney will not return to action for three weeks as he recovers from an ankle injury that saw him carried out of training on Tuesday.
He moved to Old Trafford from Everton in 2004 for £25.6m and has helped the club win three successive Premier League titles from 2007-09. His previous contract was due to expire in the summer of 2012.
From BBC
Source: http://www.manutd-blog.com