The judge said Shelly Sterling had negotiated a good deal and the removal of her husband as a co-trustee was in good faith and not part of a secret plan to seize the team.
Shelly Sterling hugged her lawyer and wept after the judge explained his ruling from the bench.
"I can't believe it's over," she said. "This is the best thing."
An unusual provision of the ruling bars Donald Sterling from seeking a court-ordered delay of the sale as he appeals. His lawyers plan to seek permission from an appellate court to file an appeal.
Sterling was not in court for the ruling. Bobby Samini, one of his lawyers, said Sterling reacted calmly to the news and told his lawyers they had to keep battling on other fronts. Sterling testified during the case that he would fight the NBA until his death.
With lawsuits pending in state and federal courts, the ruling in Los Angeles County Superior Court is unlikely to put an end to the bizarre saga that began in April when a recording surfaced of Sterling scolding his young girlfriend for bringing black men to Clippers games.
The NBA moved quickly to ban Sterling for life and fined him $2.5 million.
Sterling was apologetic after the audio recording went viral, but his mea culpa backfired when he criticized Lakers great Magic Johnson, who had been photographed with Sterling's girlfriend, as a bad role model for kids because he had HIV. Sterling was roundly condemned from locker rooms to the Oval Office, where President Barack Obama called Sterling's remarks "incredibly offensive racist statements."
With the NBA threatening to seize the team and auction it, Sterling initially gave his wife of 58 years permission to negotiate a sale but then refused to sign the $2 billion Ballmer deal, which would be a record price for an NBA team. He said he would sue the league instead and then revoked the trust, which his lawyers said effectively killed the deal.