Duffy joined Finsbury last September as chief operating officer following a management restructure on the departure of CEO Dave Brooks.
Duffy, who was previously managing director of WT Foods, had considerable experience in the industry, said Finsbury, adding that he had "ably assisted" Martin Lightbody, who has been CEO since Brooks' departure.
Lightbody will become non-executive chairman on 25 November, when chairman David Marshall will step down from the role. Marshall will become deputy chairman from that date.
Finsbury this week reported a 2% increase in full-year like-for-like sales. Adjusted pre-tax profits for the year to 30 June dropped 35% to £5m, although sales rose 8.4% during the period to £178.9m.
The company blamed a difficult trading environment and costs associated with reorganising the business for the drop in profits.
"We have spent the past year integrating our business to drive improvements in efficiency and service," said Lightbody.