Keane, 34, who is out injured for two months with a broken metatarsal bone in his left foot, revealed the news in a television interview, saying he would leave after 13 years at United when his current contract runs out in the summer.
He did not say explicitly that he would be joining Celtic, although that is clearly understood to be his preferred destination, and United are privately willing to fight to keep their captain. However, his acceptance that injuries are slowing him down suggests that Keane is now resigned to leaving.
He has admitted in the past, not least in his controversial autobiography, that joining Celtic would represent the fulfilment of a childhood dream and Keane said yesterday that a move away from United would allow him to prolong his career for another two seasons. He also added that he would be "surprised" if United were prepared to give him a new contract.
His current one-year deal, which runs out in July, is the second extension of the four-year contract he signed in December 1999 that earns him around £2.5 a year. He signed the second of two one-year deals in April this year and the expectation at United was that they would start negotiating a similar contract in the new year.
Keane said: "I would be surprised if United offered me a new deal. It's my gut feeling that if United did offer me a contract it would be around April and that will be too late. I would like to have something sorted out by January. I would like to play on for another year or two and it would be good experience for me to play at another club or in another country.
"When I say playing for another team, I can't see it being an English team. That would be too hard to stomach." Although Keane dismissed any prospect of a coaching role at United, the club hierarchy would be in favour of him going away to another club to gain experience and then returning to Old Trafford in a coaching capacity.
Sir Alex Ferguson, the United manager, is understood to support any move to keep the experience of Keane within the club, yet even if the player leaves next summer he would not be closing the door on a possible return in the future.
There is also a feeling within the club that the interview given by Keane - broadcast on the club's in-house MUTV channel - may have been a way of kick-starting negotiations on a new deal. It is a tactic that Keane has used in the past to bring United to the table, but this time the words the Irish international has chosen appear to be paving the way for his exit.
Keane said: "I would like to go into coaching and experiencing a different changing-room would help that. I will be 35 in the summer and there are good players coming through at United and the time would be right. Sometimes it's better to make a clean break. People have mentioned coaching at United but it doesn't appeal to me."
Keane's words will almost certainly cause United to explore the possibility of signing him to a new deal and the club have always enjoyed an excellent relationship with the player and his lawyer Michael Kennedy.
However, Keane will know that United chief executive David Gill has a policy of signing players over the age of 30 to one-year contracts that are heavily based on performance-related pay. Keane's age and his increasing susceptibility to injury would mean a steep cut in his basic pay.
United would be likely to offer him a deal that involved him playing a threshold of around 20 games. If he exceeded that his earnings would go up considerably. Phil Neville was on a similar incentive-based contract before he left for Everton this summer and Ryan Giggs is understood to be on the same kind of deal.
Even if United do lose Keane in the summer they will, despite his protests, not give up on bringing the player back in some capacity. Keane, who has been studying for his Uefa B licence coaching badge with Giggs and Gary Neville at the club, has always been touted as a future manager at United.
The midfielder broke his toe in an innocuous challenge with Luis Garcia in the goalless draw with Liverpool at Anfield on 18 September. In the past, he has overcome serious injury problems - including a ruptured cruciate ligament that ruled him out for an entire season. But in September 2002 he had a hip operation that limited the amount of games he has been able to play ever since.
Keane has been part of seven of Ferguson's eight Premiership-winning seasons - second only to Giggs - after he was signed from Nottingham Forest for £3.75m in July 1993, just one month after United's first league title in 26 years.
He famously walked out of the Republic of Ireland's 2002 World Cup campaign, only to resume his international career last season. The question of replacing Keane, who has 64 international caps, has long been regarded as the key to sustaining United as a force in the Premiership and Europe. Ferguson has tried players such as Juan Sebastian Veron and Eric Djemba Djemba in the position, as well as recently converting striker Alan Smith, but with limited success.
The new owners of the club, the Glazer family, will now be under increasing pressure to make funds available for a replacement. Michael Ballack of Bayern Munich, who will be available for free next summer, is an obvious candidate, as is the Saint Etienne midfielder Didier Zokora.