Mack, 26, spent his first five seasons with the AFC South rival Indianapolis Colts. His best season came in 2019, when he ran for 1,091 yards and eight touchdowns on 247 carries.
Mack joins running backs Rex Burkhead, Royce Freeman and Scottie Phillips on the Texans' roster. Houston kept five running backs on the 53-man roster to start the 2021 season, but the unit struggled in Tim Kelly's offense. The Texans finished the season last in the NFL in Football Outsiders' rushing DVOA.
The 2017 fourth-round pick tore an Achilles in the 2020 opener and missed the rest of the season. The Colts that year had drafted running back Jonathan Taylor, who replaced the injured Mack and finished third in the NFL in rushing yards behind Derrick Henry and Dalvin Cook.
Mack played in just six games for Indianapolis last season and requested a trade before the Nov. 2 deadline.
In his NFL career, Mack has run for 2,484 yards and 20 touchdowns on 567 attempts. He also has 57 catches for 448 yards and two touchdowns.