NBA commissioner Adam Silver revealed the news at a press conference in New York this afternoon after investigating the recording released by TMZ last week.
Sterling is heard on the recording telling girlfriend V Stiviano in a heated argument that he does not want her to bring black people to games at Staples Center.
The $2.5m fine is the maximum that the league can impose.
Silver said that he will urge the board of governors to force Sterling, 80, to sell the franchise, which is thought to be worth more than $1 billion.
Silver, who took over as commissioner from David Stern earlier this year, also said that when he first heard the tape he hoped it had been altered as he has known Sterling for over 20 years.
Sterling has owned the Clippers for almost 33 years - the longest tenure of any NBA owner.
The Clippers play their first game at home since the news broke later tonight when they take on the Golden State Warriors in game five of their first-round Western Conference playoff game. The best-of-seven series is currently locked at 2-2.