The Giants announced the deal on Tuesday night. Terms were not disclosed.
The 30-year-old Stewart is Carolina's all-time leading rusher with 7,318 yards, and his 51 rushing touchdowns rank second in team history.
He immediately becomes the most accomplished running back on New York's roster. Orleans Darkwa, who led the Giants in rushing last season, is a free agent. Wayne Gallman and Paul Perkins are also on the roster.
''I am very pleased that we were able to make Jonathan a New York Football Giant,'' general manager Dave Gettleman, who previously had the same job with Carolina, said in a statement. ''He is a quality runner with power and speed and brings a veteran, professional presence to our locker room. He's a terrific addition for us at this time.''
Stewart was the 13th overall selection in the 2008 draft. His best season was in 2009, when he rushed for 1,133 yards and 10 touchdowns.