The Minister for Transport, Shane Ross, has welcomed the latest move.
Mr Ross said: “I welcome the news that Monday’s proposed bus strike has been called off. I would like to thank both employer and employees involved in this dispute for accepting an invitation from the Workplace Relations Commission to return to talks.
"I am sure the travelling public will be relieved that Bus Éireann services will be available to them on Monday.”
The unions involved in the Bus Éireann dispute have agreed to attend talks at the Workplace Relations Commission.
Commuters faced chaos from Monday as Bus Éireann workers stage an all-out and indefinite strike.
The NBRU and SIPTU have agreed to suspend the industrial action while talks are going on.
General Secretary of the NBRU, Dermot O'Leary, said: "We have in deference to the WRC suspended our strike action planned for Monday to coincide with the decision of Bus Eireann not to implement unilateral non-agreed measures from Monday.
"We will of course endeavour, on behalf of commuters and our members, to work towards resolving this crisis, however, the attitude displayed by Bus Éireann management to-date has left us with no option but to advise our members that they should remain on a war-footing and be prepared to engage in an immediate all-out strike, should the company plough ahead with its Irish Ferries style attack on bus workers moderate terms and conditions."
SIPTU's Willie Noone said: "It has always been apparent that the expertise of the WRC will be required to deal with the serious and complex issues in this dispute.
"In deference to a request by the WRC the scheduled strike action by SIPTU members in Bus Éireann, which was due to commence on Monday, has been suspended.
"SIPTU representatives will continue to play their part in trying to avert a national public transport dispute but we rely on the management of Bus Éireann making genuine efforts to reach a resolution."
Bus Éireann issued a statement saying that the financial situation at company "remains critical", with the company facing insolvency by May.
They said: "To facilitate meaningful discussions with unions, Bus Éireann management have today accepted a new invitation by the WRC to seek a solution.
"We will therefore defer the implementation of changes announced in our recent letter to staff, due to commence on Monday 6th March, while talks continue."