Goldman Sachs — also an early investor — was the exclusive advisor on the deal, according to a person familiar with the negotiations.

As of December, Plaid said one in four people in the United States with bank accounts have connected to the fintech company through an app. Visa and rival Mastercard were early investors in the start-up, along with the venture arms of Citi and American Express.

Plaid's API software, often referred to as the " plumbing " behind fintech companies, lets start-ups connect to users' bank accounts. It's well-known among financial technology developers, but the average person interacting with it most likely wouldn't recognize the name. High-profile Plaid customers include popular peer-to-peer payment app Venmo, mobile investing app Robinhood and cryptocurrency exchanges Coinbase and Gemini.

Plaid raised $250 million in a 2018 Series C funding round that launched its valuation to $2.7 billion. It also added widely followed venture capitalist Mary Meeker to the board of directors.

In a call with investors Monday, Visa CEO Al Kelly said Plaid has seen a compound annual growth rate of roughly 100% since 2015. Kelly said the deal was a "long-term" play and would position Visa for the next decade. It will help expand the company's own total addressable market and relationships with fintech companies, as well as boost Plaid's growth, according to Kelly.

"This fits well, strategically," Kelly said about the acquisition. "We're excited about new businesses and the ability for this to accelerate our revenue growth over time."

Visa said the deal has the potential to add as much as 100 basis points to the company's net revenue growth by 2021.The Wall Street Journal first reported the Visa acquisition.

Plaid has grown steadily with its list of customers since it launched in 2013. The company says it integrates with more than 11,000 banks and connects to more than 200 million consumer accounts. While it does not give specific numbers or a full list of companies, Plaid said its customer base doubled from 2017 to 2018 and has expanded to the U.K. and Canada.

CEO Zach Perret told CNBC the Plaid team got to know Visa through its initial strategic investment, which was a "jumping off point for a series of conversations" leading up to the deal. Perret, who co-founded the company with a former Bain colleague William Hockey, said the Visa brand would help Plaid scale its products and global footprint.

"We feel fortunate to have been there for the early days of fintech, and to have helped develop that ecosystem," Perret said in a phone interview. "This represents an important milestone, and the ability to work with Visa to make our products products much bigger and better — both domestically and internationally."