The latest deal was negotiated through the night and came just a day after Worldpay revealed it been approached by Vantiv and JP Morgan Chase.
Worldpay raised £2.5 billion in October 2015 when its shares began trading on the London Stock Exchange.
If the Vantiv-Worldpay merger goes ahead, Worldpay shareholders would own approximately 41 percent of the share capital of the combined group on a fully diluted basis.
Vantiv's offer will see it pay 385p a share for Worldpay, or £7.7 billion, plus £1.4 billion to cover debts.
The companies will effectively merge, with Charles Drucker taking on a role as executive chairman and Co-CEO and Philip Jansen as Co-CEO.
Worldpay sells technology that enables businesses to take payments via cards, online or mobile devices - with 400,000 customers in 126 currencies across 146 countries.
Worldpay said in a statement Wednesday that it had agreed a deal in principle with Vantiv.
Worldpay Group PLC's stock soared almost 30% Tuesday, becoming the star performer in the U.K.'s FTSE 100 as two suitors approached the payments processor about a potential merger.
Several other equities research analysts also recently commented on WPG. The total value of transactions handled by the company grew 14 percent to 14.9 billion pounds in 2016, while revenue increased 15 percent to 4.5 billion pounds and pretax profit rose to 264.1 million pounds. The combined company would also expand Vantiv's footprint in the U.S., Europe, Asia-Pacific and South America, the boards said. Worldpay rival Nets AS said last week that it had been approached by suitors.
"The Boards of Worldpay and Vantiv have identified substantial opportunities for cost synergies, which support significant potential shareholder value creation."
Worldpay Group plc is a United Kingdom company, which provides a range of technology-led payment services and products.