Uber, which has faced criticism over safety issues, began operating in the city on Friday.
Glasgow City Council granted the firm a one-year licence on condition that all drivers and vehicles are appropriately licensed.
It comes on the day a High Court judge in London ruled that the controversial minicab-hailing app is legal.
Transport for London (TfL) sought clarification as to whether or not the smartphone app breaks the law by operating in the same way as meters used by more strictly regulated black cabs to calculate fares.
Authorities in Europe have criticised Uber over safety issues but the California-based firm insists its drivers are safe and reliable and required to pass enhanced Disclosure and Barring Service (DBS) checks.
Uber's UK head, Max Lines, said: "We're a private hire operator and we only use private hire drivers and private hire vehicles so all the drivers are going to be background checked.
"From a customer perspective, customers love it and drivers love it, we've seen huge growth. What we're bringing to them is a system that is very safe and very efficient and what we see is drivers actually earning good money because the system means that they are very well utilised."
Mr Lines acknowledged that the system had proved controversial for some city-based taxi firms.
He said: "We're coming into markets that maybe haven't seen innovation for quite a long time and that to me is the disruption.
"What we're trying to do is bring in new technologies, new ways of doing things and I think because of that it can be seen as disruption. But what we're trying to do is make it easier and better for both riders and drivers to get around."
Passengers are required to download the app and create a rider account before they can request a car. Once the taxi is booked, the driver's photo, name and car registration will appear on the app, along with real-time information about the car's location. Passengers are then notified when the car arrives.
Glasgow has joined London, Manchester, Birmingham, Leeds, Newcastle, Bristol, Merseyside and Sheffield in offering the service.
A controversial smartphone app which allows passengers to hail a taxi using a mobile phone has launched in Glasgow.