Kelly, who was a tryout player during the team's rookie minicamp earlier this month, has a history of off-the-field problems.
He was released by the Denver Broncos the day after he was arrested for criminal trespassing for entering a couple's home in October 2018. Kelly, a seventh-round pick by the Broncos in 2017, pleaded guilty to misdemeanor second-degree criminal trespassing in March. He was sentenced to one year of supervised probation and 50 hours of community service.
Kelly was kicked off Clemson's football team for arguing with coaches during the spring game in 2014. He pleaded guilty to a misdemeanor charge of disorderly conduct after he was arrested for a bar fight in 2014. Kelly was in another fight at his brother's high school football game in New York in October 2016. Videos showed Kelly being held back by the coaches.
Kelly spent his rookie season in 2017 on injured reserve due to knee and wrist injuries suffered while at Ole Miss. He played one snap prior to his release from the Broncos last season.
Jim Kelly and Colts coach Frank Reich were teammates with the Buffalo Bills from 1986 to 1994.
Andrew Luck and Jacoby Brissett are the top two quarterbacks on the roster. Chad Kelly will compete with Phillip Walker to be the third quarterback. The Colts kept only two quarterbacks on the active roster last season, with Walker on the practice squad.