Shelly Sterling announced late Thursday night that she has signed an agreement to sell the Los Angeles Clippers to former Microsoft chief executive Steve Ballmer for $2 billion.

A source close to the situation told ESPN's Ramona Shelburne that Sterling and Ballmer signed the final papers of the sale shortly before midnight at the offices of her Los Angeles-based attorneys. Sterling announced she was acting under her authority as the sole trustee of the Sterling family trust, which owns the Clippers.

"I am delighted that we are selling the team to Steve, who will be a terrific owner," Sterling said in a statement. "We have worked for 33 years to build the Clippers into a premiere NBA franchise. I am confident that Steve will take the team to new levels of success."

Donald Sterling bought the Clippers in 1981 for $12.5 million.

Ballmer, who previously had been involved in a failed bid to buy the Sacramento Kings and relocate them to Seattle, released a statement saying he was "honored" by the opportunity.

He has said both publicly and privately that he will not relocate the Clippers from Los Angeles.

"I love basketball," he said. "And I intend to do everything in my power to ensure that the Clippers continue to win -- and win big -- in Los Angeles. L.A. is one of the world's great cities -- a city that embraces inclusiveness, in exactly the same way that the NBA and I embrace inclusiveness. I am confident that the Clippers will in the coming years become an even bigger part of the community."

Shelly Sterling became the sole trustee of the Sterling family trust very recently, sources told Shelburne and ESPN's Darren Rovell, when her husband, the Clippers' controlling owner, was found by experts to be mentally incapacitated. Initially, both Sterlings were the trustees, but the findings by neurologists made Shelly Sterling the sole trustee, empowering her to sell the team to Ballmer.

The rules of the trust did not require a court hearing first to declare Donald Sterling, 80, incapacitated. That allowed Shelly Sterling to negotiate directly with Ballmer and the league to sell the team.

The agreement will be sent straight to the NBA for final approval, sources told Shelburne. It must be approved by the league office, and Ballmer must be approved by three-fourths of the league's owners.

Donald Sterling's lawyer, Max Blecher, confirmed that evaluations were performed on his client, but he wrote to Shelburne in an email Friday that the results of the neurologists' examinations were "grossly exaggerated" and that "Mr. Sterling is far from mentally incompetent." In similar comments to CNN, Blecher said it was determined that Sterling had "modest mental impairment," "a slowing down." The evaluations were performed earlier this month, a source told Shelburne.

Blecher also told CNN that Sterling "doesn't want a fight with Shelly. That's the bottom line."

Bobby Samini, another attorney for Donald Sterling, told the Los Angeles Times, "There's been no sale. There can be no sale without Donald's signature."

Former Microsoft CEO Steve Ballmer signed an agreement to buy the Clippers for $2 billion. Noel Vasquez/GC Images/Getty Images

Shelly Sterling and Ballmer proceeded with their deal, despite the threat of legal action by Donald Sterling, because they were, as one source put it, "very confident the sale would go through" even if there were "bumps in the road or delays."

Shelly Sterling had pushed to negotiate a sale before Tuesday's board of governors meeting at which both of the Sterlings' ownership interests could be terminated, while Donald Sterling had vowed to fight the league's attempts to force a sale. Through his personal attorney, Donald Sterling sent a 32-page response to the league this past Tuesday, but the rebuttal did not address Sterling's mental capacity as part of his defense. Shelly Sterling told the "Today" show earlier this month that she thought her husband might have been developing dementia.

Blecher had told ESPN in an interview Wednesday that "when this thing first happened, [Donald Sterling] was kind of like in a trance. It was like a state of shock. His whole system was disoriented."

Sterling's mindset at that time led to a May 22 letter from his longtime personal attorney, not Blecher, informing the NBA that his client intended to sell the team and had given his wife authority to negotiate for him. Blecher said Sterling had changed his mind since then and "as time has evolved, he's come to a much more hard-line position" and "was the old Don I knew. ... Now he says, 'Look what they've done to me. I'm not going to take this lying down.'"