The deal is expected to be completed next year
The Irish Stock Exchange (ISE) based in Dublin has been sold to pan-European exchange Euronext for €137m.
The company already runs the exchanges in Amsterdam, Brussels, Lisbon, London and Paris.
Euronext says it has acquired 100% of the shares and voting rights of ISE.
The transaction is subject to regulatory approvals, and is expected to be completed in the first quarter of next year.
In a statement, Euronext says: "The transaction brings together two highly complementary businesses with significant growth opportunities and expands Euronext’s federal model to a new attractive European country.
"It creates a leading global player in debt and fund listings, combining the listing expertise of ISE with the traded markets expertise of Euronext."
It also says the Dublin exchange is in "ideal positioning" to take advantage of post-Brexit opportunities.
"The acquisition of ISE by Euronext, combined with Ireland’s very competitive economic environment, will further strengthen Ireland’s position as a strong European anchor to take advantage of Brexit opportunities.
"This transaction will also develop the Irish capital markets ecosystem within a European context and as part of Euronext’s core mission to power the real economy."
"Dublin will have a strong group-wide position within Euronext’s highly inclusive federal governance structure, notably as the global centre of excellence for all Euronext’s group-wide activities in the listing of debt, funds and ETF securities", it adds.
Stéphane Boujnah, chief executive officer and chairman of the managing board of Euronext, said: "The Irish Stock Exchange joining Euronext represents a major milestone in the expansion of Euronext’s federal model since its IPO.
"ISE brings to Euronext leading global positions in debt, funds and ETF listings markets.
"As part of Euronext, ISE’s growth initiatives will be reinforced with Euronext’s full support.
"We are delighted to welcome Deirdre Somers and her team to Euronext."
Deirdre Somers, chief executive officer of ISE, said: "This is a landmark day in the 224-year history of ISE and a great day for our customers and our people.
"This transaction recognises the significant value and leading market position that has been built by the ISE.
"More importantly, we believe that Euronext is the perfect partner to enable us to achieve our growth ambitions."
As part of the deal, Ms Somers will join Euronext's managing board - and Padraic O'Connor, non-executive chairman of ISE, will be proposed as a new member of Euronext’s Supervisory Board.
The Central Bank of Ireland, the ISE’s regulator, is also expected to join Euronext's College of Regulators.