However, he needs a "period of intensive care to aid his recovery".
According to AFP, news of his operation was made public by his old club, with a United statement cautiously optimistic about the prospects for the 76-year-old, the most successful manager in British football history.
Ferguson began his managerial career as a 32-year-old at East Stirlingshire before going to St Mirren, where he won his first trophy by taking the Scottish first division title in 1977. "Thoughts are with the family and close ones".
Sir Alex's son Darren, manager of League One side Doncaster, did not attend his side's final home game of the season against Wigan due to his father's illness. So much part of my life personally and professionally for over 30 years. He is a regular at horse racing meetings, has co-written two books, lectured internationally, attended the Oscars and watches the majority of United matches at Old Trafford, entertaining his guests in the directors' box before and after games.
Hired from Aberdeen in 1986, Ferguson held onto his United job despite taking until 1993 to end the club's title drought.
He became Manchester United manager later that year.
Ferguson's teams dominated the Premier League and were crowned champions of Europe on two occasions, in 1999 and 2008. "He's a really good friend as well", Schmeichel said in 2013. Stay strong boss. Thoughts are with you and your family.
"Not surprised everyone has come out with these best wishes and we are all hoping for the best possible outcome for him". I was hoping it wasn't true. "Sending prayers and love to Cathy and the whole family".
Ferguson also told his former left-back Patrice Evra, now at West Ham United, that his grandchildren guided him to watch his impression of Bob Marley on Instagram.
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After the victory, he was honoured with a knighthood, meaning in Britain he was universally known as "Sir Alex".
FC Barcelona too wishes a speedy recovery for Sir Alex.
United defender Chris Smalling: Gutted to hear the news about Sir Alex. Be strong, Boss!" Eric Cantona sent a message that read: "All my thoughts, my energy, my minutes and my seconds to you boss.
Fittingly, Ferguson's treatment and recovery will be carried out near to the place where he masterminded the rebuilding of United.
"We wish him all the best and that he recovers quickly".
There was no further update on his condition on Sunday evening, although his former club Manchester United thanked the football community for its expressions of concern.
Several football clubs such as Manchester City, Leicester City, AC Milan and Al Ahly SC wished Ferguson a full and quick recovery after the surgery.
The end of Beckham's United career came after a weird incident in which Ferguson kicked a boot in the player's direction, cutting him over his eye.