They later traded him with Chuck Mount, John Davis, and Melido Perez to the White Sox for Floyd Banister and Dave Cochrane.

Hibbard only made 6 relief appearances as a White Sox, but did pick up his one and only career save.

He did not last long in Florida, as they traded him that same day to the Cubs for Alex Arias and Gary Scott.

In his lone season with the club, he finished with a 15–11 record, which earned him a 3-year deal with the Seattle Mariners.

This biographical article relating to an American baseball pitcher born in the 1960s is a stub.