Houston announced the move on Wednesday morning. The Texans signed free agent running back Troymaine Pope to the practice squad, placed running back D'Onta Foreman on injured reserve and waived quarterback Josh Jackson from the active roster.
The Cardinals waived Ellington on Monday. Ellington, 28, entered the NFL as a sixth round pick by the Cardinals in the 2013 NFL Draft.
Ellington could serve as a backup option to Texans starter Lamar Miller on Monday. The Texans are on the road in Week 12, facing the Baltimore Ravens at 8:30 p.m. on Monday Night Football at M&T Bank Stadium in Baltimore.
"Special thanks to all my fans that supported me throughout my career in AZ," Ellington wrote on Instagram Tuesday. "It's been real! I truly enjoyed my journey as a Cardinal and playing in front of you guys. Unfortunately, some things must come to an end. To my teammates, best of luck and wish all of you nothing but success going forward. Much love!."
The Texans have the No. 6 rush defense in the NFL this season, averaging 128.5 rushing yards per game.