The 38-year-old Beckham joined Manchester United's academy and spent 17 years at the club, playing 394 games with the first team and winning six Premier League titles and the 1999 Champions League under Ferguson.
"As I have said many times before, the boss wasn't just the greatest and best manager I ever played under," Beckham was quoted as saying on the website of his current club, Paris Saint-Germain.
"He was also a father figure to me from the moment I arrived at the club at the age of 11 until the day I left. Without him I would never have achieved what I have done in my career."
Beckham's relationship with Ferguson had a bitter end with the midfielder moving to Real Madrid in 2003, a few months after the manager had kicked a boot that hit him in the face.
Beckham, however, said he was grateful for the support Ferguson gave him when he came under fire following his 1998 World Cup quarter-final dismissal against Argentina, considered a factor in England's elimination.
"After '98 without the manager I would have found it virtually impossible to cope with the attention I was getting on and off the field, and for this I will always be grateful to him for his support and protection," Beckham said.
"I am truly honoured to have been guided by the greatest manager in football and to have had the career that I had under him. Thank you boss and enjoy the rest!"
The 71-year-old Ferguson has managed Manchester United for more than 26 years, leading Britain's most-supported club to 13 English league title, two European Cups, five FA Cups and four League Cups, as well as the FIFA Club World Cup.
Everton manager David Moyes is the favourite to replace him.
