Alexander took over as owner on July 30, 1993, and the Rockets went on to win back-to-back titles in 1994-95. In 24 seasons under Alexander, the Rockets have won 56.9 percent of their games, fifth-highest in the league.
Brown said the 74-year-old Alexander had been approached over the years by potential buyers, but never considered it until very recently.
"It's been something he's been thinking about a little bit," Brown said. "It can wear on you after so many decades and he's tired. There are passions in his life now that are becoming more and more clear. His family, certainly, and his philanthropic efforts, what he'll be able to do with his additional time and his resources on a global scale is something that he's very much looking forward to."
Brown will be working with the league office while they look for a new owner. There is no set timetable for the sale, but Brown said they want to find the right buyer and won't rush the process.
Included in the sale will be Clutch City Sports and Entertainment, which puts on non-basketball shows and concerts at the Toyota Center.
"It's a nice opportunity to have that rolled into one asset," Brown said.