The deal is for $21 million and includes $10 million fully guaranteed, a source told ESPN's Adam Schefter.
Callahan's 2018 season ended in December, when he broke his left foot in the Bears' 15-6 victory over the Los Angeles Rams in a Sunday night game.
Callahan, 27, emerged over the past three years as a valuable member of the Bears' secondary. He started 10 games last season, recording 45 tackles, two sacks, two interceptions and six pass breakups.
An undrafted free agent out of Rice in 2015, Callahan also picked off two passes in the 2017 season.
He received the 11th-best grade (81.4) among cornerbacks from Pro Football Focus last season.
ESPN's Jeff Dickerson contributed to this report.