Oglesby's firm handled media for Stroger's election campaign in the February 2 primary, which Stroger did not win. She's been a managing partner of the company since 2001.
Alderman Toni Preckwinkle won the Democratic primary and faces Republican Roger Keats and Green Party candidate Tom Tresser in November.
Olgesby replaces Pamela Munizzi, who recently retired.
Oglesby will earn about $116,000 a year in the new post.
The Associated Press contributed to this report.