Fields, who was taken 11th overall, is the sixth Bears draft pick this year to sign his rookie contract.
Fields threw for 2,100 yards and 22 TDs last season while leading Ohio State to another conference title and an appearance in the national championship game. Fields struggled in the Big Ten championship game and bounced back in the national semis before losing the title game to Alabama.
He became the second quarterback drafted by general manager Ryan Pace since he was hired in 2015. The Bears traded up a spot in 2017 to take Mitchell Trubisky at No. 2 over Patrick Mahomes and Deshaun Watson. Trubisky is now backing up Josh Allen in Buffalo after the Bears decided to let him go as a free agent.
The Bears sent the No. 20 pick and a fifth-rounder this year along with a first-rounder and fourth-rounder next year to the Giants for Fields.
The Associated Press contributed to this report.