A company spokeswoman said the service did not have a launch date as it was still recruiting a Cardiff-based team.
The GMB union said Uber would make it difficult for other drivers to earn a living and the city's Hackney Carriage Association said it would take legal action.
Cardiff council said the application had been considered "in accordance with legislation".
In a statement, Uber said it was looking forward to offering a "safe, reliable and affordable choice for people in Cardiff".
Cardiff Hackney Carriage Association chairman Mathab Khan said: "If Cardiff goes ahead with Uber we will have no option but to take legal action because the council aren't capable of controlling all these drivers.
"We have already lodged hundreds of complains to Cardiff council's licensing sectionâ€¦ there are drivers who are just flouting the law and we have considered taking them to court ourselves but the council just refuses to pass their details on to us."
Steve Garelick, GMB professional drivers's branch secretary said: "Things have worked perfectly well in Cardiff until now.
"This will over saturate the market place. It will force rates down.
"We are concerned Uber will continue to work on the very edge of what is acceptable by law."
In October, the High Court found the company does not break the law.
The court had been asked to decide whether the company's smartphones were considered meters, which are outlawed for private hire vehicles.
Uber currently operates in 15 cities and towns across the UK including London, Manchester, Leeds, Birmingham and Glasgow.
Taxi booking app Uber has been granted an operator's licence for Cardiff.