The deal, sources said, is worth $20.4 million over four years with a $13.341 million signing bonus and is fully guaranteed with no offset language in the deal.
The Browns selected Richardson, a running back out of Alabama, with the third overall pick in April's draft.
Cleveland hopes Richardson can bolster a running attack that generated just four rushing touchdowns last year while being led by Peyton Hillis. Hillis, now with the Kansas City Chiefs, failed to recapture the form he displayed in a breakout 2010 season and rushed for just 587 yards on 161 carries in 2011.
The Browns traded up in the draft to acquire Richardson with the third overall pick, sending three later draft picks to the Minnesota Vikings to move up from No. 4.
With Richardson set to join the fold, Cleveland can now turn its attention to signing No. 22 overall pick quarterback Brandon Weeden.