Many of the boxes - made famous by the Tardis in Doctor Who - have already been turned into coffee and food kiosks.
Now the people have the chance to grab their own "mini police station" as 23 of the boxes are being put up for sale by Police Scotland.
It spells the end of the famed blue boxes on the capital's streets as strict conditions stipulate they are painted a different colour within a month of purchase.
The police have teamed up with the city council to invite offers for the street furniture, which have been a familiar sight since the 1930s.
There is no set price for the structures, which are on offer in several areas of the city including the Old Town, New Town, Marchmont and Murrayfield, but last week a converted Meadows police box snack counter was being sold by private owners for £20,000.
Those interested in owning a slice of history have until October 8 to submit a written offer, including a suggested use, to Police Scotland, but the force is not bound to accept the highest offer.
Once the lucky new owners are handed the keys to the boxes they will be able to convert them, but as well as painting them a different colour, they will have to either work out a deal to keep the two-tonne items on site or move them within 30 days, as the land is not owned by the police.
And as 11 of the boxes are listed buildings, negotiations around these could prove troublesome.
Malcolm Irving, author of Edinburgh Police Boxes, whose photographs were exhibited at the Drummond Street box during the 2010 Festival, said the sale marked the end of an era.
He said: "I photographed them to capture them as they were at the time. I think it's a bit of a shame that they are all getting turned into different things.
"They are objects of architectural importance rather than anything else, but some of them are in a right state."