The Browns sent an undisclosed 2012 draft pick to the Vikings for Mitchell, a 6-foot-6, 285-pounder, who will bring depth to Cleveland's banged-up defensive line.
Mitchell played in 29 regular-season games for Minnesota, which signed him as an undrafted free agent in 2006. He recorded five sacks and forced a fumble. Mitchell played in two games this season, getting a sack against New Orleans on Sept. 9.
The teams agreed in principle to the deal Tuesday, but didn't formally announce it until Mitchell passed his physical Wednesday.
The Browns also waived defensive back Derrick Roberson.