The contract is worth $15.6 million, with $7.74 million guaranteed, sources told ESPN's Josina Anderson.
Johnson had an outstanding 2017 season, leading the winless Browns with 74 catches for 693 yards receiving. Both were records for a Browns running back. Johnson and Herschel Walker are the only running backs in NFL history with 500 receiving yards in each of their first three seasons.
Johnson's role as the change-of-pace back and weapon out of the backfield is likely to stay the same this season. The Browns signed Carlos Hyde as a free agent and drafted Nick Chubb in the second round.
Since 2015, Johnson has averaged 6.3 yards every time he's touched the ball. That and his 188 catches and 1,741 receiving yards are tops for NFL backs in that time, according to the Browns. He also has rushed for 1,085 yards.
The local chapter of the Pro Football Writers of America named Johnson the team's player of the year in 2017. He has not missed a game to injury in his career.