The move comes after the Texans waived running back D’Onta Foreman earlier this week. Foreman was later claimed off waivers by the Colts.
Johnson had been seeking a trade this offseason and had said there was nothing the team could do to change his mind.
Browns quarterback Baker Mayfield publicly criticized Johnson in June for his trade request but said last month that the two had addressed their issues and were “good.”
In June 2018, Johnson signed a three-year, $15.6 million extension with the Browns. He is under contract through the 2021 season.
A third-round draft choice of the Browns in 2015, Johnson has rushed for 1,286 yards over four seasons. He fell behind rookie Nick Chubb on the depth chart last season, and the team signed Kareem Hunt, who will miss the first eight games of 2019 for violating the NFL’s personal conduct policy.
Last week, Texans coach Bill O’Brien said that running back Lamar Miller will be the starter this season but said the backup spot was “wide open.”