The wide receiver, who had been a free agent after being released by the Oakland Raiders, has signed a deal worth $3m (£1.9m).
General manager Ryan Grigson said in a statement: "We feel great about acquiring a talented player in Darrius Heyward-Bey.
"He's big, strong and shows toughness in traffic and after the catch. He's got elite finishing speed that's as good as there is in the NFL.
"With this staff, this team and overall culture we're building here in Indy, we felt strongly that he was the right player and person at the wide receiver position for us moving forward."
Heyward-Bey had also held talks with the Detroit Lions before deciding to sign with the Colts.