The teams announced the swap on Saturday. Milwaukee received relief pitcher Bobby Wahl and prospects Adam Hill and Felix Valerio in the swap.
"Keon is a dynamic athlete with the ability to impact the game in the outfield, on the bases and with his bat," Mets general manager Brodie Van Wagenen said, according to MLB.com.
"He adds depth to our Major League roster for 2019 and into the future."
Broxton, 28, hit .179 with four home runs and 11 RBIs in 51 games this season for Milwaukee. The four-year veteran hit .220 with 20 home runs and 49 RBIs in 143 games in 2017 for the Brewers. Broxton owns a career .221 batting average with 33 home runs and 79 RBIs in 276 games.
Wahl, 26, posted a 10.13 ERA in 5.1 innings last season for the Mets. He made seven appearances and allowed six runs and nine hits, while posting an 0-1 record.
"Thank you Brewers for the love, support, and guidance through these past three years," Broxton tweeted. "It's been my pleasure to be apart of this team. My teammates, coaches, and fans have been everything and more to my family and I. Thank you all for being such amazing humans and standing by my side."
Hill had 26 strikeouts in 15.1 innings for Class A Brooklyn. The 21-year-old was the Mets' fourth-round pick in the 2018 MLB June Amateur Draft. Valerio, 18, hit .319 with three home runs, 22 RBIs and 16 stolen bases in 67 games in his first pro season in the Dominican Summer League.