North Yorkshire Police earlier issued an appeal about the theft at a store in Cayton, which happened on May 12.
They said a man had stolen four bottles of WKD and a can of lager, before fleeing without paying.
The CCTV image showed a man who officers wanted to trace in connection with their enquiries.
Issuing an update, a force spokesman said: “The man shown in the CCTV image has now identified himself to the police.”
He also thanked the public and media for their help with the appeal.