Thomas is eligible immediately and can play the entire season, Oklahoma announced via Twitter on Saturday night.
"We're really pleased for TaShawn," Kruger said in a team release. "He's worked really hard to be on course to graduate in May, and this gives him an opportunity to finish his degree and his eligibility concurrently. We're very happy to be adding an experienced player to an already veteran group."
Thomas and teammate Danuel House left Houston in the spring after coach James Dickey was replaced by Kelvin Sampson. House is awaiting a waiver to play immediately at Texas A&M.
With Thomas in the fold, the Big 12 race changes.
The 6-foot-8 power forward averaged 15.4 points and 8.1 rebounds last season in the American Athletic Conference, and is expected to slip into the lineup immediately for Oklahoma. Thomas gives Kruger and the Sooners one of the most talented starting fives in the country, with Jordan Woodard, Buddy Hield and Isaiah Cousins on the perimeter and Thomas and Ryan Spangler up front.
Oklahoma, which went 23-10 last season, opens its season Sunday against Southeastern Louisiana.