Hart has held the role since 2011, having joined the Derbyshire-based business from coffee retailer Caffè Nero, where he was md for five years.
Thorntons current chief operating officer, Barry Bloomer, will act as interim chief executive until a permanent successor is found.
The firm’s chairman, Paul Wilkinson, praised Hart for making a “significant contribution” during his tenure with the business.
“Over the past four years Hart has turned around our retail business, as well as creating and delivering the vision and strategy that will serve as the platform for the continued transformation of Thorntons into an international consumer goods business,” he said.
Earlier this year, Thorntons created two new operating boards for fast moving consumer goods and retail to boost performance and reflect business strategy.
Prior to joining Caffè Nero, Hart held senior positions at Abbey, Woolworths and ITM Communications and spent more than a decade with Dixons Group where he was responsible for its high street brands.