The US firm uses a smartphone app to connect passengers with vehicles, which could cut fares by about a third.
Uber confirmed yesterday it has applied for a licence to operate in Glasgow as well as having applied for one in Edinburgh, and is recruiting staff.
However, the company was unable to say when the services would start.
One of Edinburgh’s two largest taxi firms said it was not concerned by the move but an expert said operators could lose up to 40 per cent of their business.
The news comes hard on the heels of the launch of a black cab booking app, GetTaxi, in Edinburgh.
Uber, which already operates in London, Birmingham, Leeds and Manchester, has sparked fears in other countries about the lack of regulation of drivers and vehicles.
It switched to licensed drivers in Germany after being banned in Berlin and was temporarily banned in New Delhi after a woman accused a driver in the Indian capital of rape.
Cabbies brought central London to a standstill last summer over the way Uber fares are calculated.
However, Uber’s UK regional general manager, Jo Bertram, said: “All drivers have the same licences as private hire drivers, with an enhanced criminal records check and medical check.”
She said passengers could use the Uber app to see how close the nearest vehicle was, book a journey and pay the fare.
Ms Bertram declined to give rates but said Uber would aim to provide the “best value for money”.
She said around three staff would initially be recruited in Glasgow and Edinburgh. Uber employs up to 50 in London.
Aberdeen could be a future target for Uber, she suggested, but said it would take expansion “one step at a time”.
James Cooper, professor of urban transport regulation at the University of Missouri-St Louis, urged passengers to be cautious. Prof Cooper, who is on sabbatical from Edinburgh Napier University, said: “If a vehicle is licensed correctly, they have no problems – but how do passengers know?”
He said fares could be 30 per cent cheaper and existing operators stood to lose 20-40 per cent of their business.
Central Taxis, Edinburgh’s biggest black cab firm along with City Cabs, said the capital already had good taxi provision.
Director Tony Kenmuir said: “We cannot ignore an organisation like Uber when it is making headlines all over the world.
“However, we have reviewed the market in Edinburgh and the public is very well served by the taxi trade. There is a relatively high number of taxis for the size of population, and one of the newest fleets in the UK.”
Mr Kenmuir added: “I do not see a clear cut market for Uber here as standards are so high and vehicles are readily available.”
Glasgow Taxis, the city’s largest operator, urged passengers to stick with established operators.
Vice-chair Stephen Flynn said: “When booking a taxi, the only way to ensure a fully licensed and disclosed vehicle and driver is to use a recognised company.
“Third-party systems can’t guarantee the same level of regulation and, when passenger safety should be absolutely paramount, that is concerning.”
An Edinburgh City Council spokeswoman said: “We can confirm Uber has lodged an application for a booking office in central Edinburgh. The applicant and any objectors will have the chance to present their case before a decision is made.”
A Glasgow City Council spokesman said: “We can confirm an application for a taxi booking office has been received [and] will be considered in due course.”