The deal includes more than $22 million in guarantees, a source told ESPN's Michael Smith on Wednesday.
"Needless to say, Kelvin is very happy," Fletcher Smith, Hayden's agent, told the Indianapolis Star Wednesday night. "The [contract] just made a lot of sense for us."
Hayden intercepted three passes each of the past two seasons but is best remembered for his acrobatic interception in the Super Bowl, which he returned for a touchdown to seal the victory over Chicago.
After the Colts' playoff loss to San Diego, Hayden said he still wanted to play for the Colts but sounded uncertain about his future with the team.
Colts president Bill Polian called Hayden the team's top offseason priority.
Late last week, however, Polian said the Colts likely would use the franchise tag if they couldn't reach a deal before Thursday's deadline. That would have cost the Colts about $9.9 million and would have pinched Indianapolis' salary cap situation more than it already is.
On Wednesday night, Polian still was not sure something would get done.
Within four hours, though, Smith and the Colts closed the deal on yet another big contract. Since 2004, the Colts have signed Peyton Manning, Marvin Harrison, Reggie Wayne, Dwight Freeney, Bob Sanders, Dallas Clark, Ryan Lilja and now Hayden to deals worth $19 million or more.
But signing Hayden gives Indy more options to keep other players.
Polian can use the franchise tag on three-time Pro Bowl center Jeff Saturday. Or he could deal with a logjam of free agents, whose representatives said negotiations were stalled while the Colts tried to resolve Hayden's status.
Smith's agent, Thomas Mills, said Wednesday he did not expect the Colts to sign Smith before the free-agent market opens next week.
Polian has said this is the worst salary cap pinch the team has endured since his tenure began with Indy began in 1998, and that using the franchise tag on Hayden might have forced the Colts to begin releasing other veterans.
Michael Smith is an NFL reporter for ESPN. Information from The Associated Press was used in this report.