The teams announced the trade Saturday. Broxton had 4 home runs, 11 RBI and a .179 batting average in 51 games for Milwaukee last season.
Mets general manager Brodie Van Wagenen called Broxton, 28, a "dynamic athlete with the ability to impact the game in the outfield, on the bases and with his bat."
Wahl, a 26-year-old righty, was acquired by the Mets from Oakland in July as part of the deal that sent closer Jeurys Familia to the Athletics. He went 0-1 with a 10.13 ERA in seven games with the Mets and a combined 4-2 with a 2.20 ERA for New York's and Oakland's Triple-A teams last season.
Brewers general manager David Stearns says Wahl "has the arsenal to be a very quality major league reliever and has dominated the upper levels of the minor leagues."
Hill, a right-handed reliever and fourth-round draft pick out of South Carolina, went 1-1 with a 2.35 ERA in 9 games for the Brooklyn Cyclones last season.
Valerio batted .319 with 3 homers and 22 RBI in 67 games in the Dominican Summer League.