A representative for the two players told ESPN.com they are not allowed to transfer to another American Athletic Conference school, cannot go to another school in the state of Texas and will be unable to transfer to a school on Houston's 2014-15 schedule. All others must be approved by Houston.
Erskine McDaniel said Thomas and House will appeal the ban and apply for a waiver to play next season.
The 6-foot-8 Thomas is a junior who led the team in scoring (15.4 points per game) and rebounding (8.1), while House is a 6-7 sophomore who averaged 13.6 points and 5.3 boards this past season.
Both will attract significant interest from high-major programs on the transfer market.
The two players had their appeals Thursday morning and found out the decision early Friday evening. Both players told ESPN.com that they did not want to remain in the program following a recent coaching change in which Kelvin Sampson replaced James Dickey.