Sterling bought the team in 1981 for $12 million and presided over decades of losing seasons before engaging in a fierce legal battle with his estranged wife to hold on to his most prized asset.
The team said the sale closed after a Los Angeles court confirmed the authority of Shelly Sterling, on behalf of the Sterling Family Trust, to sell the franchise to the former Microsoft CEO.
The NBA Board of Governors had previously approved the sale.
"Really excited — in a pretty hardcore way — to continue the path to making the Clippers a better and better basketball team, and a better and better citizen of the Los Angeles community," Ballmer told The Associated Press in a phone interview.
The bizarre drama began in April when a recording surfaced of Donald Sterling scolding his girlfriend for bringing black men to Clippers games. The audio spurred the NBA to ban Sterling for life and fine 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. The 80-year-old real estate mogul 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 Ballmer deal. He said he would sue the league instead and then revoked the trust, which his lawyers said effectively killed the deal.
Shelly Sterling removed Donald as a trustee after doctors found he had symptoms of Alzheimer's disease.
Adam Streisand, Ballmer's lawyer, said Tuesday that Superior Court Judge Michael Levanas signed the order authorizing the sale even if Donald Sterling's attorneys filed an appeal.
He said even if Donald Sterling seeks an emergency order directing the judge to vacate his order, the lawyer is confident an appellate court would agree that Levanas made the correct decision.
Donald Sterling's lawyers weren't immediately available to comment.
The sale ends some troubling concerns that had surrounded the team in recent months.
Doc Rivers would possibly have quit as coach if Sterling remained the owner, interim CEO Richard Parsons had testified. All-Star point guard Chris Paul, who also is president of the Players Association, might have sat out and convinced other players to join him. Sponsors who already started to flee after the Donald Sterling recording was released might have stayed away for good.
None of that appears to be a problem with Ballmer taking over what could be a powerhouse team next season. By agreeing to the record purchase price, he's already proven he's willing to spend in contrast to the famously frugal Sterling, long regarded as the worst owner in the NBA.
"The topic of conversation with Doc earlier was to focus in on what does it take and how can I help support him in achieving our mutual mission and in a pretty intense way continue to improve, be tenacious," Ballmer said. "If we do all that, good things will come our way."
Ballmer was nearly an NBA owner last year before owners chose to keep the Kings in Sacramento, rather than allow them to be sold to a group that included Ballmer and moved to Seattle.
Now he's got his own team to share with his wife and three sons.
"We're a family that likes basketball," he told the AP.
Ballmer said he fell in love with the sport as a seventh-grader in his hometown of Detroit. He was manager of his high school team, which included keeping statistics.
Two of his sons have played the game, while the youngest has been a statistician for his high school team in the Seattle area, where the family lives.
Ballmer said he hopes to attend a lot of Clippers games next season. He said Parsons has agreed to stay on as CEO for the interim.
"That gives me a chance to figure this all out," he said.
Ballmer wants to put the controversy in the past and focus the team on being "a great citizen in the community for a diverse set of folks," including the NBA's predominantly black players.
"We're going to do our best on that," he said. "I know that is high on Doc's list, it's high on my list to do that. We also have to be a phenomenal basketball team, play really well as a team and have great success on court. We're going to work on all those things."
Ballmer agreed to give Shelly Sterling the title of "owner emeritus."
"I am confident that Steve will bring the city a championship team in the very near future," she said.
AP Business Writer Ryan Nakashima contributed to this report.