The move comes after complaints from the public and from within the trade that some of the hackney carriage and private hire drivers working in the city struggled with speaking, reading or even writing the language.
There are also fears that with the recent influx of migrant workers from eastern Europe there is a pressing need to ensure a basic literacy standard across the industry.
From today, any new driver who applies for a licence will first have to pay for a £15 test which covers literacy, language and numeracy.
If they fail the 70 per cent pass mark, they will have to get extra lessons or educate themselves before being allowed to re-take the test.
There are currently 4,200 private hire and 1,100 taxi drivers in the Leeds district. In the last six months the council received 500 applications for private hire licences.
The tests were approved by Leeds City Council's Licensing & Regulatory Panel yesterday and are backed by the taxi and minicab trade bodies and the council's own licensing department.

They will be carried out by independent assessors at the city college Leeds Thomas Danby.
Des Broster, the council's principal lead officer for taxi and private hire, told the YEP: "There are no exceptions to it (the test). It's not just about the Asian community or people from Eastern Europe.
"If somebody fails we would look to give them a sufficient time-span to pass the test, but if they don't then they will be refused the chance to apply for a licence.
"Licensing officers aren't going to get involved in conducting any tests at all. It needs to be done by an educational establishment which is why Thomas Danby is involved."
The pass mark is similar to the national Adult Literacy Test standard.
Those who fail, and are unemployed, will be offered free lessons under the Government's Skills for Life programme.
Even if they pass, applicants still have to get through a DSA driving test and Criminal Records Bureau check before finding out if they've got a licence.
Current licence holders are exempt.
Mr Broster added: "There is what's known as grandfather rights. Those members in the trade who are already existing licence holders do not have to take the test."
At yesterday's meeting, panel chair Ronald Feldman (Conservative, Alwoodley) said: "To me, if somebody wants to be a driver he should be able to understand basic English.
"We're not expecting them to be Shakespeare, but have a basic knowledge of where they're going and what it's going to cost. To learn the language of the city where they live is a bonus."
Commenting about the test, he added: "There are two types of English – English and Yorkshire English. I hope they learn a bit of both."