Van Pelt spent the past two seasons with the Bengals. Before that, he was an assistant with the Green Bay Packers, Tampa Bay Buccaneers and Buffalo Bills. He was the Bills' interim offensive coordinator in 2009.
Dan Pitcher, an offensive assistant with the Bengals since 2016, was promoted Thursday by the team to fill Van Pelt's role.
Van Pelt spent his two seasons in Cincinnati under two different head coaches. Marvin Lewis and the Bengals parted ways after the 2018 season, and Van Pelt was retained by the offensive-minded Zac Taylor, who praised Van Pelt throughout the 2019 season.
"He is, in a sense, a veteran at the position," Taylor said in December.
In addition to his years coaching in the league, Van Pelt's time playing quarterback was considered a huge asset when it came to grooming inexperienced QBs.
Kevin Stefanski, Cleveland's new head coach, was the Minnesota Vikings' offensive coordinator this season. Stefanski has not announced whether he will continue to call plays as a head coach.
The Athletic first reported the move.
ESPN's Ben Baby contributed to this report.