In the NFL title game, Nicks caught 10 passes for 109 yards as the Giants beat the New England Patriots 21-17.
Injuries have slowed the 6-foot, 210-pounder since. He played in just 13 games in 2012 while dealing with foot and knee injuries and fought through an ankle injury for 15 games last season.
While Nicks managed 56 catches for 896 yards before sitting out the season finale, he failed to score a touchdown for the first time in his professional career. During a conference Saturday morning with local media, he declined to discuss the past.
"Last year was last year," Nicks said. "I don't really want to get into that. I've got a new start now."
That new start includes a few familiar faces. Indianapolis running back Ahmad Bradshaw was a teammate with the Giants, and Colts wide receivers coach Charlie Williams was Nicks' position coach in college at North Carolina.
The receiver even has a little history with Indianapolis head coach Chuck Pagano, who was the defensive coordinator for the Tar Heels during his freshman season.
"Part of being a free agent is making the choice where you want to go," Nicks said. "We all know I'm a football player, and I feel like this is the best fit for me. The football coaches, I've heard a lot of great things about them. Andrew Luck is one of the best young quarterbacks in the game today, and I would love to play with him."