Judge Michael Levanas said the $2bn sale could go ahead.
Mr Sterling, 80, had been contesting his estranged wife Shelly's decision to sell the basketball team franchise to ex-Microsoft CEO Steve Ballmer.
Mr Sterling was banned from basketball for life after he was recorded making racist remarks in April.
The Los Angeles court case focused on allegations that Mrs Sterling used medical tests of her husband's mental capacity to remove him as a member of the trust that owned the team, and deceived him into selling.
Mr Sterling had originally agreed to the sale of the basketball team, but then revoked his blessing, saying he had been improperly removed from the trust.
Mrs Sterling had told her husband to seek an evaluation by two doctors in May. The doctors declared him "mentally incapacitated" and unfit to administer his duties as trustee of the Sterling Family Trust.
This in effect handed Mrs Sterling control of the Clippers.
Judge Levanas of the California Superior Court said he found Mrs Sterling to be a more credible witness than her husband and that she had acted properly over the sale, the BBC's Peter Bowes in Los Angeles reports.
He said that Mrs Sterling "had every good reason to believe that Donald agreed to the sale of the team".
Mrs Sterling burst into tears as the ruling was delivered after the nine-day hearing, saying: "I can't believe it's over. I feel good."
The ruling would take effect in the coming weeks, the judge said.
In a statement, the National Basketball Association (NBA) said it was "pleased" by the ruling. "We look forward to the transaction closing as soon as possible," it said.
The racism allegations had led the NBA to fine Mr Sterling $2.5m. It had also said it wanted to force Mr Sterling to sell the team.
In a 10-minute audio recording published on celebrity website TMZ in April, Mr Sterling was heard telling a woman, subsequently identified as his girlfriend V Stiviano, not to associate in public with black people nor bring them to Clippers games.
The remarks drew widespread condemnation from fans, retired basketball stars and President Barack Obama.
Mr Sterling is suing the NBA, alleging it violated his constitutional rights by relying on information from an "illegal" recording.
A US judge has ruled that the LA Clippers basketball team can be sold, despite the objections of banned co-owner Donald Sterling.