The Rockets sale would eclipse the record of Steve Ballmer's $2 billion purchase of the LA Clippers in 2014.
"I am truly honored to have been chosen as the next owner of the Houston Rockets. This is a life-long dream come true," said Fertitta, a native of Galveston and life-long resident of the Houston area.
The transaction, which includes operation of the Toyota Center Arena, requires the approval of the NBA Board of Governors.
Terms of the sale were not disclosed, other than the fact that Fertitta has no other partners in connection with the transaction.
"I am excited to welcome and pass the torch to Tilman. He is a Houstonian, business leader and committed to the success and excellence of the Rockets both on and off the basketball court," said Alexander. "I have personally known Tilman for over 24 years and don't think I could have found anyone more capable of continuing the winning tradition of our Houston Rockets."
Forbes Magazine valued the Rockets franchise this past February at $1.65 billion -- good for eighth in the NBA -- with revenues of $244 million.
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The owner of Landry's, Inc., and chairman of the Board of Regents of the University of Houston, Forbes calls Fertitta the "World's Richest Restaurateur." His net worth has been reported at about $2.8 billion.
An original investor in the NFL's Houston Texans, Fertitta offered $81 million to buy the Rockets in 1993, but the team was sold to Alexander for $85 million.
Under Alexander, the Rockets have won two NBA championships.
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"Leslie Alexander has been one of the best owners in all of sports, and I thank him immensely for this opportunity. He has the heart of a champion," Fertitta said. "Lastly, out of respect for the NBA's approval process, I can say no more other than I am overwhelmed with emotion to have this opportunity in my beloved city of Houston."
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ESPN contributed to this report.
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