Heyward-Bey's one-year deal will include a $1.5 million signing bonus, a league source told ESPN NFL Insider Adam Schefter.
"We feel great about acquiring a talented player in Darrius Heyward-Bey," general manager Ryan Grigson said in a statement.
"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, who was released by the Oakland Raiders this offseason, had visited the Colts last week.
The 26-year-old Heyward-Bey, who was drafted No. 7 overall by Oakland in 2009, had 41 receptions for 606 yards and a career-high five touchdown receptions last season.