The MP for Loughborough's remit will include oversight of the hospitality sector and see her liaising with trade bodies including UKHospitality and the British Beer and Pub Association (BBPA) on hospitality strategy and consumer affairs.
It comes as Scully, who helped spearhead the launch of the Hospitality Sector Council last year, takes up a new appointment as minister of state at the Department for Levelling Up, Housing and Communities, amid a swathe of new Cabinet appointments following Prime Minister Boris Johnson's resignation.
Writing on Twitter, Hunt said: "I am looking forward to getting started!"
Scully said he was delighted for Hunt, but added that he would miss the role.
Trade body representatives from the hospitality sector thanked Scully for his work to support businesses during the pandemic.
"Thank you for listening, engaging and working with the industry and for your help and support as the first hospitality minister," wrote Kate Nicholls, chief executive of UKHospitality.
Emma McClarkin, chef executive at the BBPA, said similar: "Thanks to Paul Scully for the support you have given to hospitality and the beer and pub sector."
Both Nicholls and McClarkin added that they were looking forward to working with Hunt.