The Texans also announced the release of offensive lineman Nick Martin on Friday.
In 11 games for the Texans last season, Johnson recorded 235 yards and one touchdown on 77 carries. The pass-catching back had a career-worst 28 receptions for 249 yards and a score.
Martin, a second-round pick in the 2016 NFL Draft out of Notre Dame, signed a three-year, $33 million contract in 2019 that included more than $18 million guaranteed. According to Spotrac, he was owed a base salary of about $7.3 million in 2021 and will have a dead money charge of $2.5 million.
The Texans saved about $6.3 million against the salary cap by cutting Martin.
After missing his rookie season because of a foot injury, Martin started 62 games over the past four seasons in Houston. The veteran center is the younger brother of Dallas Cowboys star offensive lineman Zack Martin.