The Colts announced the transaction Monday. Indianapolis waived running back Keith Ford in a corresponding roster move.
The Texans cut Foreman, who was a third-round pick by the franchise in the 2017 NFL Draft, on Sunday. The organization felt the tailback needed a fresh start and an opportunity to mature with a different team, according to ESPN.
Foreman showed promise during his rookie year before sustaining a torn Achilles tendon in Week 11 against the Arizona Cardinals. He recorded 327 yards and two touchdowns on 78 carries prior to his injury.
The 23-year-old running back played in only one game last season after spending most of the year on the physically unable to perform list due to his Achilles injury. He returned against the Philadelphia Eagles in Week 15 but was a non-factor in the matchup.
In 11 career games with the Texans, Foreman had 85 carries for 326 yards and two scores. He also caught eight passes for 111 yards and one touchdown.
Foreman will join Marlon Mack, Nyheim Hines and Jordan Wilkins in the Colts' running back group.