Koskie hit .249 with 11 home runs and 36 RBI in 97 games last season, his first with the Blue Jays after spending the first seven years of his career with Minnesota. He was on the disabled list from May 20 to July 26 because of a broken right thumb.
"Corey is a demonstrated run producer, has excellent defensive skills and brings postseason experience with him to our ballclub," Brewers general manager Doug Melvin said. "His all-around abilities will be a key ingredient to our mix as we look to get to the next level competitively."
It was the second significant trade between the teams this offseason. The Blue Jays acquired first baseman Lyle Overbay and right-hander Ty Taubenheim from Toronto for right-hander Dave Bush, left-hander Zach Jackson and outfield prospect Gabe Gross at the
winter meetings in Dallas last month.
The Blue Jays also signed a pair of expensive free agents during their busy offseason: starting pitcher A.J. Burnett and reliever B.J. Ryan.
The Blue Jays signed Koskie to a $17 million, three-year contract before last season, giving him a chance to play in his native Canada. But they had a logjam at the corner infield positions after acquiring slugging third baseman Troy Glaus in a trade with Arizona last month.
Along with Overbay and Glaus, Toronto's infield includes Shea Hillenbrand and Eric Hinske.
In eight major league seasons, Koskie has a .277 batting average with 112 home runs and 473 RBI. He helped the Twins win three consecutive AL Central titles from 2002-04.
Wolfe, a 25-year-old right-hander, went 5-2 with eight saves last season, pitching exclusively in relief at three minor league levels.