Under the terms of the takeover, FIS shareholders will control 53% of the company, with Worldpay investors owning the rest.
The combined group, which will be called FIS, will have sales of $12.3 billion and the firm expects nearly $1 billion of cost savings.
A number of payment firms have merged in recent times, including Fiserv buying First Data for $22 billion. And last week another, called Network, announced plans to float in London, led by former Worldpay chief Ron Kalifa.
Worldpay’s head office is in the heart of the City, near the Bank of England.
The company, which was founded in the late Eighties, came under RBS’s ownership before the financial crisis when it bought Worldpay owner NatWest.
However, following the financial crisis, RBS sold the company to buyout firms Advent and Bain as a condition of a state bailout.