Kenny Heron was 51 when the accident happened.
An East Lothian man died after an "industrial accident" in a Co-op shop in Perth earlier this month.
Kenny Heron, 51 and from Tranent, succumbed to his injuries on Thursday 17 October after suffering serious injuries in the incident.
The East Lothian Courier reported Mr Heron was injured while working on a lift at the Co-op store on Main Street, Bridgend, Perth on Thursday 11 October and was flown to Ninewells Hospital in Dundee by air ambulance.
Mr Heron had served in the British Army for 12 years spending six months in Bosnia and, more recently, he worked as a postman in East Lothian.
The Co-op said health and safety is a key concern and the company continues to liaise with authorities to help the investigation.
A spokesman for Co-op said: “We are very saddened to hear about the death of Kenneth Heron and no words can help ease his family’s loss, who are uppermost in our thoughts.
“We have been in touch with his employer to offer our support.”
A Police Scotland spokesman said a multi-agency investigation is ongoing.
He said: "Officers attended a shop on Main Street, Perth, on the morning of Friday, October 11, following a report of an industrial accident within the premises.
“A 51-year-old man was taken to Ninewells Hospital, Dundee, for treatment, but died of his injuries on Thursday, October 17.
“A report has been submitted to the procurator fiscal.
“Inquiries are ongoing and Police Scotland is currently jointly working with staff from Perth and Kinross Council’s Health and Safety Department.”
Mr Heron's funeral will take place at Seafield Crematorium on Thursday 7 November with a collection for the air ambulance.
Mr Heron's employers Wanzl UK have been contacted for comment.