The hard-throwing right-hander had Tommy John surgery on Aug. 4 with New York Yankees head physician Christopher Ahmad and is likely to return in late 2021 or at the start of the 2022 season.
He will make $750,000 this season as he rehabs as well as a $550,000 signing bonus, sources said, and his base salary for 2022 will be $3.45 million.
Kahnle, 31, had been one of five key relievers in the bullpen, joining Chapman, Zack Britton, Chad Green and Adam Ottavino. Manager Aaron Boone's late-inning options became limited by Kahnle's injury and Ottavino's ineffectiveness.
Kahnle struck out 88 in 61⅓ innings and walked 20 in 2019, averaging 96.8 mph with his fastball. He had a 3.67 ERA.
He threw a 20-pitch eighth inning at Washington this year in his season debut on July 26 with three strikeouts, a hit and a walk, then felt discomfort while working out on July 28 and stopped a planned throwing session the following day. He didn't pitch again this year.
The veteran reliever had refused an outright assignment to Triple-A Scranton/Wilkes-Barre and elected to become a free agent, Kahnle's right as a player with at least three years of major league service.
Kahnle is 9-9 with four saves and a 3.52 ERA in 285 appearances over seven major league seasons.
The Associated Press contributed to this report.