Word of the deal first broke when Peyton Manning mentioned it during a charity appearance.
The Patriots passed over Addai six years ago in the draft and selected Laurence Maroney, which didn't work out.
Addai, 29, is a declining player, though, who hasn't rushed for 1,000 yards since the 2007 season when he went to the Pro Bowl.
Last season, Addai tallied 433 yards and one touchdown for the Colts. And as a rookie, Addai rushed for 1,081 yards and caught 40 passes. But injuries have hampered him in recent years.
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