Batchelor is due to leave in March, when he will join Saga, the travel and insurance group aimed at the over-50s.
Once Domino’s appoints a new boss, Wild will continue in an executive role for two months – in the meantime, non-executive Michael Shallow will become senior independent director.
Chairman Stephen Hemsley said: “I am delighted that David has agreed to step in as interim chief executive whilst we continue our search for a permanent replacement.
“Since joining as a non-exec in November, he has quickly got to grips with the business and I look forward to working with him over the coming months as we continue to progress the group’s exciting growth plans.”