Taxi-drivers convicted of serious offences, such as rape, murder or dangerous driving, will be automatically disqualified from holding a licence under new measures to be enforced later this year.
The Minister for Transport, Mr Brennan, is to introduce tougher entry criteria for taxi drivers in response to fears about the safety of customers since the industry was deregulated.
There is no indication of how many current drivers will be affected by the move.
Taxi union leaders claim hundreds of people with serious criminal records have been issued with taxi plates in the last two years since the industry was deregulated, although this has not been substantiated by gardaí.
The Carriage Office, which is responsible for vetting the records of applicants for taxi licences, say there is no significant change in the number of people with criminal records applying for or being granted licences.
Insp Declan Brogan of the Garda's Traffic Division in Dublin said around one-in-seven applicants for a public service vehicle (PSV) licence have a criminal record.
However, only a fraction of these applicants have a serious criminal record.
And they are typically refused a licence, he said.
"We welcome the legislation. It clarifies the area.
"If you're refusing someone a livelihood, you have to make sure a decision is a sound one.
"This will bolster current legislation, which is between 30 and 40 years old," Insp Brogan said.
However, taxi union leaders say flaws in the current legislation and pressure on gardaí since the deregulation of the industry have led to an increase in drivers with serious criminal records being awarded licences.
Mr Vincent Kearns of the National Taxi Drivers' Union said there had been a dramatic increase in attacks on passengers by taxi-drivers.
Deregulation of the industry had given rise to low standards in both drivers and cars, he said
Under existing legislation, a number of high-profile individuals have secured licences despite opposition from the Garda, who may refuse a licence if the individual has committed a serious criminal offence or if they do not judge an applicant to be of "good character."
Mr Gerry Hutch, known as "The Monk", also won a court battle two years ago to become a taxi-driver after he proved he was a tax-compliant citizen.
The Taxi Regulation Bill, which has been enacted but not fully enforced, specifies that there will be an automatic disqualification from driving for a range of serious offences including rape, murder, manslaughter, assault, drug trafficking and sexual offences.
A separate disqualification is included for drivers convicted of dangerous driving and driving under the influence of drink or drugs.
Applicants who are refused taxi licences will still be able to appeal official decisions to the District Court under the new measures.