Los Angeles Clippers -- State Farm Is Back On Board ... Now That Donald Sterling's Gone

Steve Ballmer's purchase of the L.A. Clippers is already paying off -- huge sponsor State Farm is jumping back into bed with the team now that the old Sterling regime is dead ... TMZ Sports has learned.

A rep for the insurance giant tells us it reinstated its deal with the Clippers almost immediately after the NBA made the official announcement yesterday that Ballmer's $2 billion deal had been approved.

We broke the story ... State Farm suspended its relationship with the Clips after we posted Sterling's racist audio recordings.

More than a dozen advertisers jumped ship back in April.