Earlier this year, Sterling was stripped of his ownership by the NBA after his racist remarks became public. He spent weeks contesting the move. Shortly thereafter, Ballmer agreed to purchase the team for $2 billion.
"The NBA Board of Governors previously approved the sale and Ballmer is now the Clippers Governor," the NBA said.
"I am humbled and honored to be the new owner of the Los Angeles Clippers," Ballmer said in a statement. "Clipper fans are so amazing. They have remained fiercely loyal to our franchise through some extraordinary times."
The transaction ends Donald Sterling's run as the longest-tenured owner in the NBA after 33 years. Three years affter buying the Clippers in 1981, he moved the franchise from San Diego to Los Angeles.
The 80-year-old real estate mogul has been in probate court fighting his wife's proposed deal to sell the team. At issue was whether Sterling killed the deal by revoking the trust after his wife removed him as a trustee. Shelly Sterling acted after doctors found Donald had symptoms of Alzheimer's disease.
The drama began in April when a recording surfaced of Sterling dressing down his young girlfriend for bringing black men to Clippers games. The audio spurred the NBA to ban Sterling for life and fine him $2.5 million.
His wife of 58 years then took control of a family trust and negotiated a record $2 billion sale of the team to Ballmer. Shelly Sterling said she was initially given her husband's blessing to sell the team and he praised the deal she reached.
When it came time to sign it at the end of May, however, Sterling said he would not sell and would sue the league.
Ballmer, Microsoft's former CEO, said he will be "hardcore" in giving the team, coach Doc Rivers, the staff and players the support they need.
Rivers called it "an amazing new day in Clippers history," and said he's inspired by Ballmer's passion for the game.
—By CNBC.com with AP