Kelly was coming off a two-game suspension for violating the NFL's personal conduct policy. The ban stemmed from his October 2018 arrest for criminal trespassing after he entered a couple's home; the Denver Broncos released Kelly the next day.
Kelly, a seventh-round pick of the Broncos in 2017, pleaded guilty to second-degree criminal trespassing -- a misdemeanor -- in March. He was sentenced to one year of supervised probation and 50 hours of community service.
The Colts signed Kelly in May. The nephew of Hall of Fame quarterback Jim Kelly had a tryout with the team during its rookie minicamp earlier that month.
He played in all four of the Colts' preseason games, completing 54 of 73 passes, with two touchdowns and two interceptions.
The Colts can sign Chad Kelly to their practice squad if he clears waivers.
Information from ESPN's Mike Wells was used in this report.