The deal, which also includes the operation of the Toyota Center, requires the approval of the N.B.A.’s board of governors.

In a statement announcing the sale, the Rockets alluded to the recent devastation in Houston caused by Hurricane Harvey, saying, “It is truly unfortunate that this announcement is occurring amidst the aftermath of one of the biggest tragedies in the history of our great city.” Fertitta is a native of nearby Galveston.

The big price came in part because the Rockets are a stable and successful franchise, which won 55 games last season, led by a superstar, James Harden. It is also based in the country’s fourth-largest city.

But the value of every N.B.A. team is rising thanks to the explosion of television money. The league has a nine-year, $24 billion deal with ESPN and Turner Sports. The deal nearly tripled the annual revenue from the previous deal.

The previous record for an N.B.A. team was the $2 billion sale of the Clippers to Steve Ballmer in 2014.