Mell is expected to hold a news conference about his decision on Friday at City Hall.
Mell, 75, submitted his resignation this week. He will officially step down from his post representing the North Side ward on July 24.
The influential Chicago politician is the father of state Rep. Deborah Mell. He's also the father-in-law of former Illinois Gov. Rod Blagojevich, who's in federal prison for corruption. Mell helped Blagojevich get elected to Congress in 1996, but the two later had a falling out.
There have been rumors that Mell's daughter would succeed him, but Mayor Rahm Emanuel says there will be an open application process for the job.
The Associated Press contributed to this report.