Ex-players and the first-team squad were in attendance in honour of English football's most successful manager.
"It's fantastic, a really proud moment," said Ferguson.
The 70-year-old has been in charge of the Reds for 26 years, winning 37 trophies including 12 Premier League titles and two Champions Leagues.
"Normally people die before they see their statue, so I'm out-living death," added Ferguson.
"I've had an incredible journey at the club and I've had so many great players, some of whom are here today.
"They should build this statue for them all, because they've been absolutely marvellous.
"From 1986 right through to today, the players have given us enormous pleasure.
"Everyone has had a part to play, from the players to the coaching staff, medical staff and, of course, the fans."Former United players Eric Cantona, Ruud van Nistelrooy, Ole Gunnar Solskjaer, Edwin van der Sar, Peter Schmeichel, Andy Cole, Dwight Yorke, Bryan Robson and Gary and Phil Neville joined fans for the unveiling while David Beckham and Cristiano Ronaldo sent pre-recorded tributes.
United chief executive David Gill said: "People can talk about many things like the hairdryer and Fergie time, but the most important thing you have brought back to this club is respect."
Revealing why Lady Cathy was chosen to unveil the statue, Gill added: "She is Sir Alex's greatest supporter. And I think he's a bit scared of her."
Ferguson thanked his wife for her support throughout his career but joked: "Cathy has promised that every Saturday morning she's going to come down here and bow to the statue!"
In a pre-recorded message, former England captain Beckham said: "What an amazing day for you, your family and for the club.
"I just want to say thank you for everything you have done for me. My time at United was without doubt the highlight of my career and I cherish it."
Real Madrid forward Ronaldo added: "Well done boss, I think you deserve it 100%."
Following the unveiling of the statue, former United and Netherlands striker Van Nistelrooy said: "All that's said today is an understatement. [His achievements are] more than anyone can describe. He's a visionary, building teams and he's done it many, many times over his 26 years."
Ex-England and United captain Robson said: "When you get an honour like that from a club as big as Manchester United you know you've been very successful and you've achieved a lot more than people could ever imagine."
Danish keeper Schmeichel, who Ferguson once described as the bargain of the century, said: "It's so well-deserved. I don't think there's a single person in this country or the world of football, who has been more influential than he has."
Former United and England striker Cole said: "He's an unbelievable man, an unbelievable manager and that's why so many people and ex-players have turned up for him today."
Fergie's United trophy haul
- Premier League 12 - 92-93, 94-94, 95-96, 96-97, 98-99, 99-00, 00-01, 02-03, 06-07, 07-08, 08-09, 10-11.
- Champions League 2 - 98-99, 07-08
- European Cup Winners' Cup 1 - 90-91
- European Super Cup 1 - 1991
- Intercontinental Cup1 - 1999
- Fifa Club World Cup 1 - 2008
- FA Cup 5 - 89-90, 93-94, 95-96, 98-99, 0304
- League Cup 4 - 9192, 05-06, 08-09, 09-10
- Community Shield 10 - 90, 93, 94, 96, 97, 03, 07, 08, 10,11