The 71-year-old Ferguson's final game in charge after 26 years at Old Trafford will be on Sunday while the 38-year-old Beckham will retire as a player after champions Paris St Germain's Ligue 1 finale against FC Lorient on May 26.
Beckham's longevity and his ability to reinvent himself were "absolutely incredible", Ferguson said.
"You talk about longevity and in many ways reinventing himself, it has been absolutely incredible," Ferguson was reported as saying by the BBC.
"When he went to America there wasn't a person in this place who really thought he could have a career," Ferguson added about Beckham's move to LA Galaxy in 2007.
"Yet he went on and still played for his country, he played for AC Milan in European ties and he played for PSG in European ties, and I don't think anyone could have imagined that.
"He had unbelievable stamina ... he could run all day, and that has allowed him to stay in the game at that kind of level, playing for his country in his mid 30s."
Beckham joined Manchester United as an 11-year-old and went on to play 11 years at the club under Ferguson, winning six Premier League titles and the Champions League in a trophy-laden career.
The midfielder, who described Ferguson as a father figure, had a falling out in 2003 when a boot kicked by the manager in the team's dressing room following a defeat struck Beckham in the face and the player moved to Real Madrid later that year.
"I think he's picked the right time (to retire)," Ferguson added. "He's won the league again with PSG and he is exactly the same as me, he has plenty of things to do.
"He is a young man, fashion will be his role I would imagine... He is an amazing person."
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