The team also waived rookie running back Armond Smith.
Ogbonnaya played in two games for the Texans this season, carrying three times for six yards. He was originally drafted in the seventh round in 2009 by St. Louis, where he was with Browns coach Pat Shurmur. Ogbonnaya spent the first 11 weeks of his rookie season on the Rams practice squad before appearing in two games.
The 6-foot, 225-pounder played college ball at Texas, where he was a teammate with Browns quarterback Colt McCoy.
The Browns may have signed Ogbonnaya as protection with Peyton Hillis nursing a strained hamstring he hurt in the first quarter of Sunday's loss at Oakland. It is not known how long Hillis will be sidelined.
Smith had three carries for two yards.