Taoiseach Enda Kenny has told the Dáil that over €10m, which was allocated for the mobility allowance and the motorised transport grants this year, will be ring-fenced for a new scheme that will be legally compliant.
Mr Kenny said that the Government had no choice but to close the grants to new applicants and that it would spend the next four months devising the new scheme.
The schemes will be closed to new applicants with immediate effect.
Those currently in receipt of the mobility allowance will continue to receive it for another four months.
Fianna Fáil leader Micheál Martin told the Dáil that 5,000 people would be affected by the move and described it as scandalous and reprehensible.
Earlier, Minister of State Kathleen Lynch said the Government "agonised" over its decision to scrap schemes, but had no choice.
The minister said that they were illegal and could have cost the Exchequer between €170m and €300m to extend eligibility to them in order to comply with the Equal Status Act.
Ms Lynch said she was aware of the hardship the decision would impose.
However, she said the Government could not afford to extend the scheme and could not continue to operate outside the law.
She said that HSE is conducting a review into the transport needs of those in receipt of the payments, and that the "only reassurance" she could offer them is that those needs will be met into the future.
The minister also said that a "full Government approach" was being taken to examine how to introduce a universally accessible transport system.
Decision came as 'bolt out of the blue'
Ombudsman Emily O'Reilly has said the Government gave no indication it was going to scrap the mobility allowance and motorised transport grant scheme.
Ms O'Reilly said the decision came as a "bolt out of the blue".
The Ombudsman previously found that the schemes were being operated illegally by the Department of Health and the HSE.
Their operation contravened the Equal Status Act because they excluded applicants over 66 years and she had recommended that they be brought in line with the law.
After initially accepting her recommendation in April 2011, Ms O'Reilly said the department said last year that these changes would be too expensive.
However, she said that just three weeks ago Minister for Health James Reilly and Minister Lynch gave no indication that the schemes would be scrapped when they appeared before an Oireachtas committee.
Instead, Ms O'Reilly said they had announced that a review group would be set up to examine the schemes and bring them in line with the law.
The Ombudsman said she understands that the decision to scrap the scheme followed advice from the Attorney General.
In a statement last night, Ms O'Reilly said she hoped that the Government's promised review of the transport needs of people with disabilities would proceed as speedily as possible.
She said it is entirely regrettable that the department's failure to tackle these matters in a timely, coherent and rational manner has now imposed hardship on more than 5,000 people with disabilities, who will find their transport needs compromised when the schemes are discontinued.
Disability Federation CEO 'appalled' by decision
Disability Federation of Ireland CEO John Dolan said he is "appalled" at the decision to discontinue the schemes.
Speaking on RTÉ's Morning Ireland, Mr Dolan said that news of the cut had come "out of the blue", and compared it to the consultation process that preceded the new agreement on the public service agreement.
"We have here, no consultation, no engagement, out of the blue comes a statement that says people who are living on less than €200 a week, €10,000 a year, with an extra at the max of this scheme, an extra €2,500, will have that taken away, that's a 20%, an up to 20% cut," Mr Dolan said.
"This strikes right at the heart of people who are already, like everyone else, struggling to make ends meet."
Mr Dolan said that despite a three-year review of the Department of Health's Disability Services Programme, the department choose not to review these travel allowances, even though it was aware of the Ombudsman's concerns that their terms were too narrow.
He was critical of what he called the department's "Bart Simpson approach" where he said it seeks to blame others for the decisions it makes, which have a negative impact on those with disabilities.
"This department is a sick bureaucratic monster, if you go back to last August it blamed the Troika for taking €10m out of PA (personal assistant) services for people with disabilities, yesterday and today it's blaming the equality legislation and the Ombudsman.
"There is a major issue for a Government that says it's beyond Kathleen Lynch and it's beyond the Department of Health.
"There's an issue here for the Government to get to grips with a department that seems to be coming up with a Bart Simpson approach to everything, it's always someone else's fault that we have to screw people with disabilities to the floor."
Disability rights campaigner Suzy Byrne described the decision to end the schemes as a "disgrace".
She said the decision will hit those on waiting lists for the allowances very hard.
Up to 4,700 people receive a mobility allowance and 300 receive a motorised transport grant.