In exchange, the Browns got the Colts' first-round selection in the 2014 NFL draft.
The blockbuster move came after Indianapolis starter Vick Ballard suffered a torn knee ligament during a practice session last week, leaving a gaping hole in the Colts' offense.
The 5-foot-9, 225-pound Richardson -- taken by Cleveland third-overall in the 2012 draft -- has started all 17 games for the Browns since then, racking up 1,055 yards and 11 touchdowns on 298 carries.
He also has hauled made 58 catches for 418 yards and one touchdown.
Richardson was instrumental in helping the Crimson Tide capture national championships in 2009 and 2011, recording 3,130 collegiate rushing yards and 35 touchdowns on 540 attempts.