LONDON — The financial technology provider Fidelity National Information Services agreed on Monday to buy Worldpay for about $34 billion, in a bid to become a powerhouse in the global payments sector.

The deal is among the biggest in the industry, as companies race to capture a share of the booming payments market. Companies like Worldpay are often invisible to consumers, but they process the escalating number of e-commerce transactions and purchases made through contactless payment systems like Apple Pay.

That growth has already driven some big deals. In January, Fiserv agreed to buy another big processor, First Data, for about $22 billion.

Acquiring Worldpay, a former unit of the Royal Bank of Scotland that itself has grown through acquisitions, would give Fidelity National Information Services — known as FIS — a formidable presence in the e-commerce market. Worldpay says that it processes about 40 billion transactions a year.