The Tigers acquired outfielder Justyn-Henry Malloy and left-hander Jake Higginbotham. The swap at the winter meetings came after Jansen, who led the NL with 41 saves last season, left the NL East champion Braves and got a $32 million, two-year deal with the Boston Red Sox.
Jimenez, who turns 28 next month, was 3-2 with two saves and a 3.49 ERA in 62 games with the Tigers last season, striking out 77 in 56 2/3 innings. The right-hander has spent all six of his seasons in the majors with Detroit and was an All-Star in 2018.
The 22-year-old Malloy hit a combined .289 with 17 home runs and 81 RBI at three minor league levels last season.
The 26-year-old Higginbotham was 2-5 with a 4.73 ERA in 48 relief appearances at Double-A Mississippi.