The news was first reported by the Los Angeles Times' Andrew Greif.
The deal completes a major hurdle in the Clippers' effort to construct a new arena in Inglewood, Calif., something Ballmer has pushed for since he purchased the team for $2 billion in 2014.
“This is an unprecedented time, but we believe in our collective future,” Ballmer said in a statement. “We are committed to our investment in the City of Inglewood, which will be good for the community, the Clippers, and our fans.”
In early March, ESPN's Kevin Arnovitz reported that the two sides were nearing a deal.
"The Clippers continue to pursue plans to build a state-of-the-art, 18,000-seat basketball arena and entertainment complex in Inglewood and are currently working with the city to successfully complete the comprehensive Environmental Impact Report," the team told ESPN in a statement regarding the prior report.
"We are examining every possible way to resolve our differences with Madison Square Garden Co. regarding our new arena."
MSG acquired The Forum in 2012, but it has dealt with legal battles in recent years, namely as it relates to the Clippers building a new stadium nearby.
In 2017, Los Angeles agreed to a deal with the city in hopes of developing an arena complex just south of the Rams' new stadium.
Per Greif, the deal will also resolve litigation brought by MSG, which attempted to block the Clippers’ proposed privately funded, arena.
The Forum will continue to operate as a music venue until a new Clippers arena is finished, per the official release.
An NBA team hasn't regularly played in The Forum since 1999, when the Lakers moved to Staples Center. The Los Angeles Sparks played in The Forum from 1997 until 2001, when they also moved to Staples Center.