Four different representatives from the taxi trade asked the council for various increases in the price of journeys following a steep decline in drivers.
Following a two hour discussion, the authority’s licensing committee agreed hikes and to review the fares every year around January.
It is the first time the fares have increased since 2016.
Councillor Karen McGowan, chair of the licensing committee, said: “You do offer value for money and thank you for that.
"I hope members of the public appreciate the service you offer. My experience is you do offer value for money and the service you provide for wheelchair access is very much appreciated.
"I hope this fare increase helps you to continue the good work you’re all doing.”
The fares will increase from March 1 but council officers said it would need to go back to review if there were objections before February 24.
What are the new black cab fares in Sheffield?
These are the tariffs for the first 100 yards:
Tariff one – day time (7am until 7pm) £3.10.
Tariff two – night time (7pm until 7am) £3.30.
Tariff three – weekends (7pm until 7am) £4.30.
This increases by 20p for every 195 yards up to 17,600 yards.
There will also be 20p added for every 48 seconds the cab driver is kept waiting.
Prices will increase on bank holidays and there is a £50 charge for ‘fouling’ a cab.
Why are taxi fares increasing?
Black cab drivers asked for the increase to help them cope with increasing costs and competition.
Ibrar Hussain, who has been a cab driver for 34 years and is a former councillor, said costs such as fuel and road tax had shot up and with the cost of upgrading vehicles to be compliant with the Sheffield Clean Air Zone, which is due to be implemented this year, drivers were leaving.
Mr Hussain said: “The costs are so high for me to stay in a Hackney carriage and provide a quality of service.
“We have gone from 857 cabs down to now 600 and the trend is downhill and that will continue with the [Clean Air Zone] coming in as well. I think we could end up with only 200 cabs.”