The Texans announced the signing Tuesday on social media. The team, however, didn't provide details of the agreement.
Burkhead is the seventh running back on the Texans' roster, joining standout veterans Mark Ingram, David Johnson and Phillip Lindsay. Houston added Ingram and Lindsay earlier this year in free agency after restructuring Johnson's contract in March.
The 30-year-old Burkhead spent the past four seasons in New England, where new Texans general manager Nick Caserio was director of player personnel. Houston hired Caserio in January after his 20 seasons with the Patriots.
Burkhead appeared in just 10 games for the Patriots last season before injuring his knee against the Texans. He becomes the ninth former Patriots player added by Caserio since he took over as Houston's general manager.
Before his injury, Burkhead recorded 274 rushing yards and three touchdowns. He also caught 25 passes for 192 yards and three receiving scores.
The Cincinnati Bengals selected Burkhead in the sixth round of the 2013 NFL Draft out of Nebraska. He has notched 2,545 total yards and 22 touchdowns over 82 career games with the Bengals and Patriots.
In the 2020 season, the Texans -- led by David Johnson and Duke Johnson -- ranked last in rushing DVOA, leading to Houston's increased focus on its running game this off-season.