The company said there was “huge demand” for the service, with more than 65,000 people in Edinburgh already opening the app.
Customers have to download and create an account with the app, which then allows them to book, track and pay for journeys.
The app, which launches at 4pm, matches customers up with the closest driver using their smartphones, and has faced criticism from traditional taxi companies
Earlier this year, the city council granted Uber a licence to run a booking office from George Street, which is required by law for licensed taxis or private hire companies. But in August the company said it was delaying its Edinburgh launch after struggling to find “the right people” to run its office operation.
There are also plans to expand the service to Aberdeen and other Scottish towns and cities.
Uber said a journey from Edinburgh Airport to the Balmoral Hotel would cost about £16, and a trip from Edinburgh Castle to the Royal Yacht Britannia around £8.25.
Les McVay, company secretary of City Cabs – the Capital’s oldest taxi company – said he “welcomed” the competition.
But he insisted Uber’s cut-price costs were unsustainable in the long run.
He said: “That’s business. It’s what the public want and the public have a choice. It keeps us on our toes, and keeps our drivers on their toes.
“It doesn’t worry us. We’ve had the competition before.
“I was here to experience the competition from the private-hire side.
“We just have to compete on the level of service we are giving the public at the moment, and keep that up. We already offer an app booking service.
“What we offer is what any other app company offers.
“We already provide the service – the only thing we can’t offer is the level of discount.”
Max Lines, Uber’s general manager for UK expansion, said: “We have been blown away with the reception we received in Glasgow, so are really excited to be launching in Edinburgh today.
“Thousands of Scots have embraced Uber over the last few weeks and we hope to continue this success in the Scottish capital.
“In the last six months alone over 65,000 people in Edinburgh have opened the app, so we know there is a huge demand for the service in the city.
“At the push of a button, people will be able to get a ride which is convenient, safe and affordable. Uber also enables professional drivers the opportunity to partner with us and become their own bosses – choosing when and where they work.”