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Sir Matt, who is 59, told a news conference at the club's ground at Old Trafford: "It's time to make way for a younger man... a track-suited manager".
He said the pressures of managing a top-class team were becoming too great for a man of his age and he would now take on the role of general manager.
"United is no longer just a football club," he said, "it is an institution. I feel the demands are beyond one human being."
The new team manager has not yet been chosen but one man that may well be considered for the job is Wilf McGuinness, a former United wing-half, a coach and manager of England Under-23s.
Munich air tragedy
Sir Matt is English football's longest serving manager. He took over United in 1945 and has since had a superlative record of achievement.
With the £1 million in profits he has since made for the club he rebuilt Old Trafford, which had been badly damaged by the blitz.
He has managed three highly successful teams. The first won the 1948 FA Cup Final against Blackpool.
The second team of talented young players, known as the "Busby Babes", included Bobby Charlton and Duncan Edwards.
In 1958 tragedy struck when eight players were killed in an air crash at Munich after competing for the European Cup against Red Star Belgrade in Yugoslavia.
Sir Matt was seriously injured but survived, along with Charlton who said of him today: "Matt Busby's presence will always be at Manchester United. He is Manchester United."
After the Munich tragedy, Sir Matt built up his third team, which included the transfer of Denis Law from Italian side Torino for a record fee of £116,000.
In May last year United beat Portuguese team Benfica 4-1 to win the European Cup - the first English side to do so.
In June Sir Matt was awarded a knighthood.
Sir Matt never quite left the helm of Manchester United. As general manager he appointed Wilf McGuinness as his successor.
But Sir Matt's act proved too hard to follow and the general manager sacked McGuiness after just 18 months.
He was followed by Frank O'Farrell who fared little better, and then in 1972 Tom "the Doc" Docherty took control and gradually lifted the team's flagging performance as ageing players like Sir Bobby Charlton retired to let in new blood.
Docherty was sacked in 1977 after it was revealed he was having an affair with the wife of the team's physiotherapist.
From 1980 until 1993 Sir Matt was president of the club. He died in 1994.
There is a statue of him at the ground he helped recreate at Old Trafford, situated in Sir Matt Busby Way.
Sir Alex Ferguson, who took over as manager in 1986, led the club to a string of victories at home and abroad. In the 1998-9 season, United became the first British club to win the Premier League Championship, the FA Cup, and the European Cup.
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