The 36-year-old sharpshooter, formerly of the San Antonio Spurs, signed a two-year deal with the Rockets that the Houston Chronicle said Friday is worth $3.9 million.
A report on the Rockets' Web site said Barry, a free-agent who had been sought by other teams, decided Thursday to accept Houston's offer.
The 6-foot-7 guard, a 14-year NBA veteran, is the son of Hall of Famer Rick Barry and the brother of Jon Barry, both ex-Rockets.
"Brent is a proven winner who brings a wealth of championship experience," Rockets owner Leslie Alexander said.
"His playmaking and long-range shooting abilities are an ideal fit for Coach (Rick) Adelman's system, while his versatility allows us to use him in a variety of roles. Brent has been a consistent scorer in the playoffs and played a vital part in winning two NBA Finals championships."