McGahee's addition, which earlier was reported by ESPN NFL Insider Adam Schefter and NFL.com, helps to fill the void created when running back Trent Richardson was traded to the Indianapolis Colts for a 2014 first-round pick.
McGahee will play Sunday against the Minnesota Vikings, a team source told ESPN's Schefter. Cleveland's offensive system under Norv Turner is similar to the one McGahee played in at Baltimore and he picked it up quickly Thursday, the source said. Cleveland's coaches aren't sure yet how much McGahee will play and won't know until after watching him Friday in practice.
McGahee had been the Denver Broncos' starting running back the last two seasons but was released by the team in June. He was set to make $2.5 million in 2013 before he was let go by Denver.
McGahee, 31, suffered a significant knee injury last season that sidelined him for the final two months.
A two-time Pro Bowler, McGahee rushed for 731 yards in 10 games for the Broncos last season and has gained 8,097 in his nine-year career. He has become one of the NFL's most dependable runners despite tearing all the ligaments in his left knee during his last game in college.
Information from The Associated Press was used in this report.