The sale includes the Toyota Center and is subject to approval by the NBA Board of Governors.
Alexander put the Rockets up for sale in July. He purchased the franchise back in 1993 for $85 million, overseeing the team to its only two NBA championships in 1994 and 1995.
"I am excited to welcome and pass the torch to Tilman," Alexander said in the team statement. "I ... don't think I could have found anyone more capable of continuing the winning tradition of our Houston Rockets."
Fertitta - with an estimated net worth of $2.8 billion - owns the Golden Nugget casino chain as well as several restaurants. He also hosts a CNBC reality show, "Billion Dollar Buyer."