Clippers owner Donald Sterling was banned from the sport for life after he was recorded making racist remarks.
The NBA later agreed to begin the process of selling the team.
The bid was reportedly accepted by Donald Sterling’s wife, Shelly.
Steve Ballmer is believed to have outbid two rival groups for the team, one of which was led by media mogul David Geffen and included talk show host Oprah Winfrey.
He retired from Microsoft in February, but he still owns shares in the company.
A forced sale of the LA Clippers would require the approval of three-quarters of the 30 team owners in the NBA.
But Donald Sterling could still oppose the sale in the courts, according to sports lawyers.
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