Hitchens had 80 tackles and an interception in 15 games last season.
Hitchens, 29, joined the Chiefs as a free agent in 2018, and he registered a career-best 135 tackles that season. In four seasons with the Chiefs, Hitchens played in 70 games in the regular season and playoffs with two sacks, one interception and two forced fumbles.
The Chiefs will save about $8.4 million against their salary cap in 2022.
"I really enjoyed the opportunity to coach Anthony over the last four years," coach Andy Reid said in a statement. "He's as tough as they come in this league and is a team-first player. I appreciate the way he came to work, ready to do his part, but also his willingness to teach the younger guys around him."
Before joining the Chiefs, Hitchens played four seasons for the Dallas Cowboys. In 63 regular-season and playoff games for the Cowboys, Hitchens had 3.5 sacks, one interception and two forced fumbles.
"He has all the intangibles and was an integral piece in our franchise winning a Super Bowl title," general manager Brett Veach said in a statement. "We appreciate everything he's done for the organization and wish him the best as he continues his career."