Overnight parking, from 6pm to 8am, will also be free.
Local businesses have been lobbying hard for this change, which was announced at the Weymouth and Portland Chamber of Commerce breakfast meeting on 2 October.
The news was broken by Chris Greaves of Weymouth and Portland Borough Council, where it was greeted with a spontaneous round of applause from the 60 or so members and guests present.
It's hoped that the offer of free town centre parking will encourage more visitors to the town, bringing a welcome boost to local trade.
Privately owned car parks may still charge on Sundays and overnight, as will car parks controlled by the Crown Estates. This includes the Portland car parks at Chesil Beach, Portland Bill and Castletown.
