The city's licensing committee ordered that any black cab or private hire driver who uses the technology must warn his or her fares that they may be recorded.
But a majority voted down a bid by Green councillor Martha Wardrop to put the decision to permit taxi spycams on hold until the public had been consulted.
Glasgow City Council carried out a consultation, which asked the views of trade bodies, the police and Britain's privacy watchdog before going ahead with the plan.
A spokesman said people from Glasgow are regularly caught on camera - and microphone - on buses, trains and other public places.
He said: "As part of the consultation we took advice from the Information Commissioner and they were satisfied that privacy concerns had been properly addressed.
"Use of CCTV has a longstanding legal basis and is already commonly accepted on other forms of public transport such as buses and trains."
Taxi and private hire firms can now go ahead and install equipment to record video and audio in their vehicles.
However, audio should only be used when the driver fears he is in danger.
Councillors also decided new guidelines under which drivers must warn their customers they are on candid camera - verbally as well as in signs.
Any driver abusing CCTV rules could lose his or her licence.
Taxi and private hire operators argue CCTV could protect drivers - and members of the public.
Councillor wardrop called for passengers to be consulted first.
She was backed by SNP councillor David Turner, who said: "It would appear that while the policy aims to improve both driver and passenger safety, the council has not given passenger the opportunity to formally comment on its content.
"On this basis, it seems reasonable to put forward a proposal for a public consultation on the policy to ensure that passengers are able to submit their views on the use of CCTV to record images and make sound recordings within taxis.
"There is a requirement to raise awareness of the policy, and scrutinise the conditions to be adhered to by taxi operators."
Mr Turner said: "It is only fair we should hear from potential passengers."
Ms Wardrop's proposal was rejected by six votes to three.