Chapman, a three-time All-Star, has 113 saves over parts of five seasons with the Reds. He has 430 strikeouts over 252 2/3 major-league innings, for an average of 15.3 per nine innings. In 2014, Chapman recorded 36 saves and struck out 106 batters in 54 innings.
Chapman had filed for $8.7 million in arbitration, while the Reds had countered with an offer of $6.65 million. His settlement with Cincinnati came before a scheduled arbitration hearing Friday.
Earlier this week, the Reds avoided an arbitration hearing with third baseman Todd Frazier when they signed him to a two-year, $12 million deal.