Giggs revealed his bitter-sweet emotions in an open letter to the club's fans on a day when it was also confirmed he will take up a role as assistant to new Old Trafford manager Louis van Gaal.
Ferguson hailed the "fantastic career" of a player he signed to his first professional contract on his 17th birthday in 1990, while Beckham called Giggs an "amazing servant" both to United and the game in general.
The 40-year-old announced his retirement after 24 seasons, a record 963 appearances, 168 goals and 34 trophies for United - a record which makes him the most decorated player in English football history.
He also won 64 caps for Wales and not only captained his country but led a Great Britain side at the 2012 Olympics in London.
Giggs said: "I am immensely proud, honoured and fortunate to have represented the biggest club in the world 963 times and Wales 64 times.
"My dream was always to play for Manchester United, and although it saddens me to know I won't be pulling on a United jersey again as a player, I have been lucky enough to have fulfilled that dream playing with some of the best players in the world, working under an incredible manager in Sir Alex Ferguson, and most of all, playing for the greatest fans in world football.
"For me, today is a new chapter filled with many emotions - immense pride, sadness, but most of all, excitement towards the future.
"United fans I hope will share and echo my belief that the club, the management and owners, are doing everything they can to return this great club to where it belongs, and I hope to be there every step of the way.
"To the greatest fans in world football, thank you
I have loved every minute of playing for you and representing the biggest and best club in the world."
Giggs was a member of United's famous 'Class of '92' group of FA Youth Cup winners, and played his last game earlier this month against Hull in one of the four games for which he was in charge on an interim basis.
United's executive vice-chairman Ed Woodward said: "Ryan Giggs has been one of the greatest players ever to wear the red shirt of Manchester United.
"What he has achieved will never be equalled in the English game.
"In the way he played, he was the embodiment of a Manchester United player - fast, skilful, entertaining and determined to win by playing exciting football.
"His progress from the ranks of the famous 'Class of '92' to the most decorated player in this or any club's history is down to his hard work, ability and attitude.
"He is at the start of an exciting new chapter in his and the club's life but now is the right moment to reflect on the achievements of the finest British player of the last 25 years."
Source: PA