Terms of the deal were not disclosed by the Colts, but NFL Network Insider Ian Rapoport reported that the one-year pact is worth $5 million.
Grant sustained an ankle injury in the Washington Redskins' season finale against the New York Giants. He then agreed to a four-year, $29 million deal with the Ravens, only to see the contract voided on March 15.
The 27-year-old Grant has reeled in 84 receptions for 985 yards and six touchdowns in four seasons with the Redskins, who selected him with a fifth-round pick in 2014. Grant had 45 receptions for 573 yards and four scores last season.
Grant joins Pro Bowler T.Y. Hilton and Chester Rogers as the lone wide receivers under contract with the Colts. The team saw Donte Moncrief recently sign with the Jacksonville Jaguars while Kamar Aiken is a free agent.