Manbij is situated at an intersection of roads just south of the Turkish border.
It has been under IS control for more than two years.
Small numbers of IS militants are still resisting, using civilians as human shields, the alliance says.
The Syria Democratic Forces (SDF), a coalition of US-backed fighters including the powerful Kurdish YPG militia, launched a campaign to retake the northern city two months ago.
They were backed by US-led air strikes on IS positions.
After some heavy fighting, Manbij was encircled and completely cut off in June.