They were abandoned in undergrowth just off Warriston Path, near St Mark’s Park in Inverleith, and have been linked to a string of raids on Greggs bakeries and Subway branches.
The thieves are believed to have used specialist tools to cut holes in the underside of the concrete-lined units before seizing cash and discarding them next to a muddy path.
It appears the crooks attemped to burn out one of the safes, which was heavily scorched on the inside.
Police said forensics experts had examined the safes as part of an ongoing investigation into five break-ins to shops in the past month. Burglars escaped with thousands of pounds following raids on stores in Bruntsfield, Stockbridge and Pilton.
A 25-year-old has been arrested in connection with the latest theft, at Pennywell Road last week. However, officers are looking for more suspects. An Inverleith resident, who asked not to be named, contacted the Evening News after finding the stretch of undergrowth littered with safes.
The dog-walker said they had become something of a spectacle for passers-by.
“They are about 18 inches square, and [the thieves] appear to have made a little aperture to get their hands in,” he said.
“Two seem to have been done really professionally. I think they drove down to that spot because there’s a post missing.”
He said two safes had just appeared a few metres from the original one over the past fortnight.
“It’s now become a tourist attraction,” he said.
“People are going off the path to look at them.”
A police spokeswoman said that the safes had been thoroughly examined by detectives and it was not the council’s responsibility to removed them.
The spokeswoman added: “Police are investigating a number of break-ins to businesses which are believed to be linked.
“Greggs on Raeburn Place was broken into overnight on Wednesday, December 17, when the safe containing a four-figure sum was stolen.
“The safe was recovered the next day near to St Mark’s Park, and forensic work was carried out.
“Police are also investigating a break-in to Subway on Raeburn Place around 10.30pm on Sunday, January 4, where the safe containing a low four-figure sum and money from the till was taken, and the Subway on Bruntsfield Place on January 6 between 8.30pm and 11.30pm when a sum of money was removed from the safe and till.
“The Gregg’s shop on Pennywell Road was broken into on the evening of Thursday, January 8, and following this, a 25-year-old man was arrested and charged.
“Inquiries are still continuing and anyone with any information should contact Police Scotland on 101.”