The Colts hoped Funchess would return from injured reserve later in the season, but the injury never healed properly for the fifth-year player.
NFL Network first reported the agreement.
The Colts signed Funchess, 25, to a one-year, $10 million contract with the belief his 6-foot-4 frame would help quarterback Jacoby Brissett.
Before joining the Colts, Funchess entered the 2018 season as the No. 1 receiver for the Carolina Panthers, who drafted him in the second round in 2015. But his role decreased dramatically because of dropped passes and a nagging back issue.
Funchess has 164 receptions for 2,265 yards and 21 touchdowns in his career.
ESPN's Mike Wells contributed to this report.