Bus Éireann has lost the right to operate six routes on the Kildare bus corridor after an open tender was won by UK firm GoAhead.
The Kildare corridor routes affected are: 120, 120C, 123, 124, 126 and 130.
The GoAhead services are expected to come into operation by the end of this year or early next year.
The company previously won the first market opening tender for certain routes in Dublin previously operated by Dublin Bus.
National Transport Authority Chief Executive Anne Graham said that around 70 Bus Éireann bus drivers would be affected.
However, she said redundancies were not expected as the market is growing.
She declined to reveal the amount of the GoAhead bid, but said the contract had been awarded on the basis of 65% for price and 35% for quality.
She said the contract would require GoAhead to comply with all industrial relations regulations, but that did not include union recognition.
Ms Graham said that the tenders to open up the bus market were intended to deliver savings, value for money, price comparators and competitive tension in the market.
However, she stressed that this was not privatisation, as buses are not being sold, services are not being deregulated and control remains with the National Transport Authority.
She also anticipated that fares would remain the same, but that there would be service improvements for passengers, with the new operator delivering 11% more vehicle kilometres.
The companies who failed in the tender bid were Bus Éireann, Transdev City Connect, First Group plc, and Synergy (a consortium of Matthews Coach Hire, Collins Coaches and McGinleys Coach Travel Ltd).
A consultation process on further bus market opening will begin later this year.
Bus Éireann Chief Executive Ray Hernan said he was disappointed at the result, but the restructuring of the company is continuing and the final phase of driver work practice changes has been implemented.
NBRU General Secretary Dermot O'Leary has warned of "major industrial unrest" if any other routes are privatised.
He accused the Government of "pumping millions of euro of taxpayers' money into the pockets of the shareholders of large multinational corporations".
Mr O'Leary said the union will work to ensure that affected members will not be "forced to move from Bus Éireann to an inferior employer".
He said any other moves towards the privatisation of Bus Éireann routes will "not only be vehemently opposed by the NBRU, but will inevitably lead to major unrest across the public transport system".