The reshaped coin is set to enter circulation on March 28 and will result in machinery up and down the country needing to be upgraded to accept the new tender.
According to the city council, it will need to recalibrate a total of 816 pay and display machines to accept the new 12-sided coin, a process which will cost £204,000.
It comes as work also gets under way to remove 371 ticket machines which have come to the end of their lifespans.
A spokesman for the council said: “As part of a review of ticket issuing machines, a number of machines considered surplus to requirement are being been removed with the remainder to be upgraded to accept new £1 coins. The cost of machine upgrades has been accommodated within the existing transport budget.”
As it works to upgrade machines, the council has been urged to keep costs down to limit the impact on road maintenance projects.
John O’Connell, chief executive of the Taxpayers’ Alliance, said: “The council must make sure costs are kept down so that the part of the transport budget allocated to road safety and maintenance isn’t affected.”
The new coin’s arrival later this month will be followed by a period of ‘co-circulation’, during which people can spend both the new and old varieties.
From October onwards businesses will then no longer be allowed to accept the previous round coins. Edinburgh Trams confirmed it would also be upgrading its 49 ticket machines to accept the new coin, a process it said would cost around £6000.
It said this would be done in two stages in order to correspond with the change in circulation.
Over the course of March it will upgrade the software on machines to enable them to recognise the new coins.
It is expected this will take around 30 minutes per device and the machines will accept both coins until October.
After this point, the machines will have a second software upgrade and also have their coin slots changed so that customers can no longer pay with the previous £1 coins.
Lothian Buses however will not be affected by the change due to the ‘hopper’ devices on board each vehicle, which take all coins at once rather than individually.
The old style £1 coin has been in circulation since 1983.
According to The Royal Mint, there are around £1.5 billion of them still in circulation across the UK. It is hoped the new coin will be more difficult to counterfeit.