Financial terms of the deal were not disclosed. Suter had been seeking $1.25 million for the 2020 season while the Brewers had offered $825,000.
Suter, 30, was 4-0 with an 0.49 ERA in 18 1/3 innings last year in nine appearances as he returned from having Tommy John surgery in 2018.
He pitched a career-high 101 1/3 innings and made 18 starts in 2018 before tearing his elbow ligament in July of 2018. He also made 14 starts in 2017.
He is 17-11 with a 3.63 ERA in 223 innings over four seasons with the Brewers.