Rodgers-Cromartie was allowed to test the free-agent market by the Denver Broncos, but was close to agreeing a new deal with the club before they signed Aqib Talib.
After that deal fell through, the Giants stepped up their chase and have landed the signature of the 27-year-old on a reported five-year deal worth $39m (£23m).
Rodgers-Cromartie told the club's official website: "I'm glad to be here. Especially with Antrel [Rolle] and talking with the defensive coaches and the staff and even coach Tom [Coughlin], just talking with them, it's going to be good."
The 27-year-old recorded 31 tackles and three interceptions in the 2013 season.