Fertitta confirmed the deal on Twitter, calling it an "honor" to be a part of the NBA:
Fertitta also told TMZ that he'd love to bring Beyonce into the fold, saying "It would be great to have her involved in any way."
Randy McIlvoy of KPRC-TV reported the approval process could take 30-45 days, which could make the sale official around the beginning of October.
In July, Alexander released a statement through team CEO Tad Brown about his intention to sell the organization after more than two decades as owner:
"It's been my great joy and honor to own the Houston Rockets for the past 24 years. I've had the incredible opportunity to witness true greatness through the players and coaches who have won championships for the city, been named to All-Star and All-NBA teams, enshrined in the Basketball Hall of Fame, and done so much for our franchise and our fans.
"And the Houston community has been home to me; I will continue to support the charities I have made commitments to throughout the years. I'll always have a special place in my heart for the fans, partners, city officials and employees who care so deeply for this team. I've made this decision after much deliberation with my family and friends, and do so knowing the franchise is in great shape with the players, coaches and management team in place."
Fertitta showed an immediate interest in acquiring the NBA team. He told Berman shortly after Alexander's announcement he planned to explore the situation.
"I've always had an interest in the Rockets," he said. "It's one of Houston's four major teams. It would be exciting. This is my home. I've looked at other teams, but it's hard to be involved with another team when Houston is your home."
TheRichest listed the 60-year-old restaurateur's net worth at $2.7 billion. Fertitta is also the owner of the Golden Nugget casino in Las Vegas. In February, Forbes estimated the Rockets' value at $1.65 billion, the eighth-highest figure in the league.
Along with the sale process, it's been a busy offseason for the Houston front office. The team acquired point guard Chris Paul in a blockbuster trade with the Los Angeles Clippers and signed MVP contender James Harden to a massive four-year, $228 million contract extension.
If approved, Fertitta will become the 10th owner in Rockets history and inherit a team with the fourth-best odds to win the 2017-18 NBA championship, per OddsShark.