The 73-year-old Alexander bought the franchise for $85 million in 1993. Forbes valued the franchise in February at $1.65 billion -- eighth-most valuable in the league -- with revenue of $244 million.
"It's been my great joy and honor to own the Houston Rockets for the past 24 years," Alexander said in a statement Monday. "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."
"The Houston community has been home to me," Alexander said. "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."
NBA commissioner Adam Silver released a statement on Monday regarding Alexander's desire to sell the franchise.
"Leslie Alexander is a true competitor who always searched for the right move to make his teams better, Silver said. "Under his ownership, he created a culture of excellence with strong management that attracted Hall of Famers, All-Stars and coaching giants and brought two NBA championships and four WNBA titles to Houston.
"Well-respected around the league, he has been an active and influential owner whose vision helped to grow the game globally, especially in China. Moreover, his philanthropy speaks just as powerfully as his ownership, with local libraries, women's centers and homeless shelters all benefitting from his generosity."
Alexander put CEO Tad Brown in charge to "oversee the sales process with the league office, supported by my management team."
Brown made the announcement during Monday's news conference at Toyota Center. He said Alexander told him "it can wear on you after so many decades."
"When he mentioned to me this morning that he had made up his mind that this was what he wanted to do, I was very surprised," Brown told reporters. "But, at the end of the day, nothing truly surprises me because Leslie is a man of many passions and he's got things he wants to do and opportunities that he wants to pursue."