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 UEFA 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".
Former United midfielder Ray Wilkins hailed the decision to keep Giggs in a position of power at Old Trafford. Wilkins told Sky Sports News: "Ryan knows what Manchester United are all about and Louis has been very clever in appointing him. He knows what the club is all about.
"Ryan Giggs has worked for the last 20-odd years with the best coach the world has ever seen in Sir Alex Ferguson, so he has learned off the very, very best. It is also key the likes of Paul Scholes, Phil Neville and Nicky Butt will remain at Old Trafford as well."