Terms were not disclosed, but McAfee told "NFL AM" on the NFL Network that he has agreed to a five-year deal.
The Colts made McAfee their franchise player last year and he played the 2013 season under a one-year tender.
McAfee, a seventh-round pick in the 2009 draft, holds Colts career records with a gross punting average of 45.6 yards and a net average of 38.4 yards.
McAfee averaged 46.0 yards with a 38.5-yard net on 76 punts last season. He set a single-season record with 27 punts inside the 20-yard line, including a team-record six during a Week 7 game against Denver.
In addition, McAfee had 41 touchbacks on 86 kickoffs.