Browns coach Eric Mangini told reporters Wednesday that he thinks Mitchell could be a fit at outside linebacker.
Mitchell will first need to adjust to Cleveland's 3-4 defense, which he has never played in.
"Big difference," Mitchell told the Akron Beacon Journal. "I'm going to have to get adjusted to it."
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 the New Orleans Saints on Sept. 9.
Mitchell was surprised by the trade.
"It's shocking," he told the Beacon Journal. "I didn't see it coming at all."
The teams agreed in principle to the deal Tuesday, but they didn't formally announce it until Mitchell passed his physical Wednesday.
The Associated Press contributed to this report.