Wright, 30, was in the final year of a three-year, $18 million deal with the Grizzlies. He was officially waived by Memphis on Saturday.
Wright will become another lob target for Rockets duo James Harden and Chris Paul, providing depth behind starting center Clint Capela along with Nene and Tarik Black. His ability to finish above the rim fits well with a Houston team that features two of the NBA's premier playmakers.
Wright fell out of the Memphis rotation after being sidelined for close to a month by a groin injury, as the Grizzlies began to focus on developing young talent. He has a clean bill of health as he prepares to head to Houston.
A 6-foot-10 shot-blocker, Wright is averaging 5.0 points and 3.4 rebounds in 27 games this season for Memphis.