Ferguson, who signed Giggs on his 17th birthday in 1990 and saw him become the most decorated player in United's history, hailed his "fantastic career".
In a video message on United's official website, the Scot said: "What a fantastic career - the number of games you have played, the trophies you have won, the help you have given young people and the help you have given me and all the coaching staff."
Giggs' former team-mate David Beckham paid tribute to the Welshman's remarkable loyalty to Old Trafford.
Beckham said: "Amazing servant to the game of course, but more importantly, an amazing servant to Manchester United
We are all proud of you - Manchester United fans love you."
Another former team-mate, Gary Neville, said he doubted whether Giggs' record of 13 Premier League winners' medals and two Champions League winners' medals - plus three FA Cups and two League Cups - would be beaten.
Neville said: "Well done for everything you have achieved at the club
It is wonderful what you have done and I don't think your achievements will ever be surpassed."
Former United assistant manager Mike Phelan believes Giggs is set for a top-flight role in his own right in the near future.
Phelan told BBC Radio Five: "Ryan is Manchester United through and through, and today is a day of condolences as well because he has actually retired from playing at the ripe old age of 40
"His career has been magnificent but he can now focus on the next phase of his career which is hopefully coaching and managing.
"He definitely has experience on his side and he has the name and the clout behind him because of who he is and what he has achieved.
"I think (Premier League management) is the natural progression for Ryan, and I think it will happen in the next two or three years."
FIFA president Sepp Blatter paid tribute to Giggs via his official Twitter account
He posted: "Ryan Giggs has retired
Remarkable career by a loyal, legendary @ManUtd entertainer
963 games
34 trophies
1 club".
Source : PA
Source: PA