The blockbuster deal will create a leading international e-commerce payments provider that will process about USD 1.5 trillion in payments and 40 billion transactions per year in 146 countries and 126 currencies, they said in a statement.
The new group - which will be called Worldpay - will have a combined stock market value of approximately 22.2 billion pounds.
"The boards of directors of Vantiv and Worldpay are pleased to announce that they have reached agreement on the terms of a recommended merger of Worldpay with Vantiv ... In the form of a recommended offer," they said in a statement to the London Stock Exchange.
The new company will have its global and corporate headquarters in Cincinnati, Ohio, while London will be its international base.
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Vantiv will pay 397 pence per share for Worldpay, or 8 billion pounds, plus another 1.3 billion pounds to cover debts.
"This is a powerful combination that is strategically compelling for both companies," added Charles Drucker, Vantiv president and chief executive.
"It joins two highly complementary businesses, and will allow us to achieve even more together than either organisation could accomplish on its own.
Worldpay chief executive Philip Jansen added that the deal would offer "substantial opportunities to capitalise on the rapid evolution of payments".
The deal will "offer more payment solutions to businesses, whether large or small, global or local, enabling them to meet consumers' increasing demands", he added.
Drucker will be executive chairman and co-chief executive of the new group, with Jansen as co-chief executive.
The combined company will have a secondary listing on the London stock market, but will have its primary listing in New York.
The group was then floated on the London stock market in 2015.
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