Terms were not disclosed.
Grant, 28, struggled to find a niche in the Colts' offense last season, as it didn't take long for him to slide down the team's depth chart.
The thought last season was that Grant would come in with extra motivation and solve the question on who would be the Colts' second receiver to go with T.Y. Hilton after the Baltimore Ravens decided against signing Grant after the team said he failed his physical.
Grant battled an ankle injury during the season and his role diminished as the season progressed. He finished with 35 receptions for 334 yards and 1 touchdown. Grant had nine receptions for 65 yards in the final eight games of the season.
He spent the first four years of his career with the Washington Redskins and had 84 receptions for 985 yards and 6 touchdowns in 64 games.
ESPN's Mike Wells contributed to this report.