Yahoo! Sports' Jeff Passan reports that the deal is worth $8.05 million. Chapman's arbitration case was the last one for the Reds this season.
Chapman, 26, had an 0-3 record with a 2.00 ERA, 36 saves in 38 chances with 106 strikeouts last season for Cincinnati Reds.
He suffered a fracture about his left eye and nose and had a plate inserted in his head to help the injury heal.
Chapman, a three-time All-Star, has 113 saves with a 2.32 ERA in five MLB seasons, all with Cincinnati.
- Scooby Axson