Mitchell, who enters his fifth NFL season, was also acquired by general manager John Dorsey in Kansas City, reuniting the two in Cleveland.
Mitchell will sign a three-year, $12 million deal according to Schefter after starting nine of the 15 games he appeared in last season that saw him tally four interceptions, 18 pass breakups and 47 tackles.
The Cowboys drafted Mitchell in the seventh round of the 2014 NFL draft but he did not make the team. He bounced back and forth between Dallas and Chicago over two years and also spent time with Houston before the Chiefs picked him up in 2016.
In 30 games - 11 starts - Mitchell has totaled five interceptions, 27 pass breakups and 74 tackles.