It is the latest deal in a rapidly consolidating market where the Swiss Exchange has bid for its Madrid counterpart and the London Stock Exchange is buying financial market data company Refinitiv.
Cboe, the biggest pan-European share trading platform, already owns 20% of EuroCCP.
It is buying out the four 20% stakes held by exchanges Euronext and Nasdaq, Dutch bank ABN Amro and The Depository Trust & Clearing Corporation (DTCC).
Chicago-headquartered Cboe said it was paying cash but declined to say how much.
Euronext said it would receive net proceeds of 9 million euros, indicating Cboe paid roughly 36 million in total.
The deal is expected to close in the first half of 2020 after regulatory approvals have been received.
The combination of Europe's biggest share trading platform and equities clearing house could raise concerns among users that a "vertical silo" is being built to squeeze higher fees out of them.
"Our plan is not to recreate the vertical silo and pull up the drawbridge and issue price rises once a year without speaking to customers," said David Howson, chief operating officer of Cboe Europe.
It would be up to Cboe customers where they want to clear trades, he added.
Cboe wants to ramp up trading and clearing in equity futures and options by investing an undisclosed sum that will dilute earnings for the next three to four years, Howson said.
Euronext also wants to expand equity derivatives trading. It said on Tuesday it would look to do this through its 11.1% stake in LCH SA, the Paris unit of LCH, the world's biggest derivatives clearing house, which is owned by the London Stock Exchange.
EuroCCP CEO Cecile Nagel said the company was making money but looking for a "step change" in strategy, which was difficult with five shareholders.
Cboe, which runs a pan-European share trading platform in London, has opened a subsidiary in Amsterdam ahead of Britain's planned exit from the European Union next month.
"If we leave on January 31, beyond that we will be looking to see how we encourage further trading through the venue," Howson said.
EuroCCP's base in Amsterdam was a consideration in the acquisition due to Brexit, he said.
Being based inside the EU puts the Cboe-EuroCCP combination in a "very good place" if the bloc sought to limit trading of euro denominated shares in London, or made it harder for non-EU clearing houses to serve EU customers, Howson said.
The EU is likely to welcome consolidation that helps make its capital market more efficient and reduce reliance on London, even if it is being driven by a U.S. exchange.
(Reporting by Bhargav Acharya in Bengaluru and Rachel Armstrong; editing by Louise Heavens and Jason Neely)
By Huw Jones
