The Colts have traded their first round pick in 2014 for Richardson after Vick Ballard joined Donald Thomas and Dwayne Allen in needing surgery.
Richardson was the number three overall draft pick in 2012 and has gone on to start 17 times for the Browns.
He enjoyed a stellar first season, rushing for 950 yards - including three 100-yard outings and 51 receptions - to break Jim Brown's rookie records from 1957. Richardson finished the year with 1,317 total yards and 12 touchdowns.
This season Richardson has managed 105 yards in his two appearances, however he will now team up with the likes of Ahmad Bradshaw and Donald Brown at the Colts.