Since being drafted 30th overall in the 2006 draft, Addai led the Colts in rushing four consecutive seasons until last season when injuries helped to hold him to 495 yards. Last season, Donald Brown led Indianapolis in rushing with 497 yards.
Earlier Saturday, the Colts signed Peyton Manning to lower-than-expected contract, clearing room for Addai's deal, among others.
The 28-year-old Addai has 5,375 yards from scrimmage and 47 touchdowns in five seasons. He also is considered the Colts' best blocker at the running back position.
In 2007, Addai became the first Colts player to gain more than 100 yards both rushing and receiving in a game in the 24-20 loss to New England. He also was a Pro Bowler that season.
Information from The Associated Press contributed to this report.