The ex-England captain rose through the ranks at Old Trafford and had previously stated his desire to see out his playing career with the club.
However, Ferguson has insisted that Beckham's celebrity lifestyle had resulted in the midfielder believing that he had become "bigger than the manager".
"The minute a Manchester United player thought he was bigger than the manager, he had to go," he wrote in his autobiography.
"David thought he was bigger than Alex Ferguson. That was the death knell for him."
Beckham went on to play for Real Madrid, LA Galaxy, AC Milan and Paris Saint-Germain prior to his retirement at the end of last season.