Ulster Bank is to begin a phased withdrawal from the Irish market, its parent company NatWest has confirmed.
Explaining the move, NatWest said a review of its Irish bank found that it would not achieve an acceptable level of returns going forward.
Uncertainty now surrounds the bank's 2,800 staff, although NatWest insists it will try to keep job losses to a minimum.
Ulster Bank's operations in Northern Ireland are unaffected by the announcement.
Two other Irish banks - Permanent TSB and AIB - have already made moves to potentially acquire Ulster Bank assets south of the border. The Irish Government is a majority stakeholder in both AIB and Permanent TSB.
"Following an extensive review and despite the progress that has been made, it has become clear Ulster Bank will not be able to generate sustainable long-term returns for our shareholders," said NatWest chief executive Alison Rose.
"As a result, we are to begin a phased withdrawal from the Republic of Ireland over the coming years which will be undertaken with careful consideration of the impact on customers and our colleagues."
The announcement came as NatWest revealed that it made a pre-tax operating loss of £351 million in 2020.
Irish Finance Minister Paschal Donohoe said it was a "difficult day" for the Irish banking sector and for the Ulster Bank staff.
Permanent TSB and other banking interests are in talks with NatWest over the potential acquisition of Ulster Bank's retail and SME assets, liabilities and operations.
NatWest has also signed a Memorandum of Understanding (MoU) with AIB over the purchase of Ulster Bank's corporate and commercial loans.
Mr Donohoe said those moves represented important developments.
"The decision by NatWest, the parent of Ulster Bank, to exit the Irish market is a very significant event," he said.
"After 160 years serving the Irish public, today marks a sad day. Our thoughts too are with the Ulster Bank staff as they learn of the closure of the bank here in Ireland.
"However, I welcome the reference made this morning to the two other Irish banks, PTSB and AIB, who are engaging with NatWest regarding the future of Ulster Bank's SME, mortgage, retail and commercial loan books, as well as the current and deposit accounts held by the Bank.
"While this is positive news and indicates the potential further development of already well established Irish banks, there is still much work to be done over the coming months."
Mr Donohoe stressed that the Government did not have any role in commercial decisions over the bank's future.
He added: "Reassurance is also given to customers of Ulster Bank that robust consumer protections are in place in the event of the bank withdrawing from the Irish market, including the Central Bank's codes of conduct and that the terms of any contract currently in place with Ulster Bank remains in place into the future.
"I also welcome the announcement regarding Ulster Bank staff which outlines that some staff will transfer to AIB in line with the MoU that has been agreed with that bank. The commitment to engage with staff to minimise the impact on them is also to be welcomed. I expect that Ulster Bank will fully engage with staff in an open and transparent manner as the process moves forward.
"The Irish banking landscape will be poorer for the loss of Ulster Bank after all these years but we will focus now on the future and what can be done to support and strengthen a competitive and stable Irish banking system for the future."
The Irish Labour Party said the move by NatWest was a hammer blow for Ulster Bank staff and customers.
The party's finance spokesman Ged Nash said: "This devastating news is a hammer blow for the 2,800 Ulster Bank staff, for their customers and for businesses across Ireland.
"My immediate thoughts and concerns are with the bank's dedicated staff whose future is uncertain. Any sale or potential merger must respect the right of staff to have their existing terms and conditions transferred with them and compulsory redundancies should be off the table."
Labour urged the Irish Government to use its majority stake in the Permanent TSB to create a new bank with the Ulster Bank assets. The party believes this "third force" bank would ensure competition in an Irish market already dominated by the two main players, Bank of Ireland and AIB.
"What we need to avoid is the piecemeal dismantling of the bank and its operations by vulture funds and other Irish banks which will damage any effort to create a real third force," said Mr Nash.
"It is incumbent on the Government and the Minister for Finance to drive such an outcome rather than acting as commentators.
"The bank and its assets are now vulnerable and any fire sale of assets to vulture funds must be categorically ruled out."