The Disclosure and Barring Service (DBS) checks, are processed by the Home Office and individual police forces. But drivers have complained that they have been unable to work - in some cases since August - because of the delays.
Today TfL said it was seeking to ease the pressure by issuing temporary licences to existing drivers who had applied for their check more than three months before their licence expired.
The licences will initially be limited to two weeks in length, although drivers can apply for a renewal.
Drivers from both black cab and private hire vehicle industries who are applying for a licence for the first time will not be eligible.
The Met has already drafted in around 60 additional members of staff to help with the backlog, which has become a major headache for taxi drivers over the last few months.
"The new measures will further ease pressure, whilst ensuring that the high standards required from drivers are maintained," TfL said.
London Mayor Boris Johnson, said: "The last thing we want to see is London's taxi drivers out of work. These temporary measures are the most effective way of tackling the immediate issue, alongside a dramatic boost to staffing levels at the Met.
"I am confident that this approach will ensure that drivers are able to get back to work as soon as possible while maintaining public safety."
Garrett Emmerson, TfL’s Chief Operating Officer for Surface Transport, said: “We are aware that a number of drivers have been unable to work due to the delays in receiving their DBS certificate, and that these delays are affecting them and their families.
“These new measures will help these drivers while ensuring that the high standards required of drivers are maintained.”
As a condition of the temporary measures, drivers will be required to sign up to the DBS update service in order to prevent a similar situation occurring in future.
The move has been welcomed by the London Taxi Drivers Association, which earlier today described it as "a victory for common sense and the LTDA".