The deal is worth $3.2 million, as first reported by Fansided.com. It includes an additional $200,000 in performance bonuses for innings: $100,000 each for 40 and 60.
The 33-year-old left-hander went 5-3 with a 3.78 ERA in 54 appearances this season. He struck out 53 and walked 22 in 66 2/3 innings.
Suter had spent his entire big league career with Milwaukee, making his debut in 2016. He was the longest-tenured Brewers player and had served as the team's union representative.
In 196 career appearances, including 39 starts, Suter is 36-19 with a 3.51 ERA. He has 338 strikeouts and 98 walks in 394 2/3 innings.
Suter was the Brewers' 2022 nominee for the Roberto Clemente Award, given to a player who best represents baseball through character, community involvement, philanthropy and positive contributions on and off the field. It was the third time the Brewers had nominated him for the award.
"Incredibly thankful for what he was able to provide to this team, our clubhouse, our community - just above and beyond what you could ever ask," Brewers president of baseball operations Matt Arnold said. "Probably the best teammate I've ever been around since I've been in the game."
The Associated Press contributed to this report.