Ajay Banga, former chief executive officer of Mastercard Inc., is joining General Atlantic as vice chairman, officials at the private-equity firm said.

Mr. Banga, who stepped down as CEO at the card network Jan. 1 after more than a decade in the role, will advise General Atlantic’s top management on the firm’s strategy and work with its sector and geographic leaders on investment strategy.

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Ajay Banga, former chief executive officer of Mastercard Inc., is joining General Atlantic as vice chairman, officials at the private-equity firm said.

Mr. Banga, who stepped down as CEO at the card network Jan. 1 after more than a decade in the role, will advise General Atlantic’s top management on the firm’s strategy and work with its sector and geographic leaders on investment strategy.

One area of focus will be on financial inclusion—providing individuals and businesses with access to useful and affordable financial products—a passion of Mr. Banga’s, according to General Atlantic CEO Bill Ford.

Mr. Banga, 62 years old, became CEO of Mastercard in 2010 and oversaw a more than 13-fold increase in the company’s market capitalization. He is credited with expanding the business into new markets around the world and transforming it through acquisitions from a predominantly card-based company to one offering a range of payment technologies.

“He’s incredibly global, has a deep understanding of emerging markets and knows financial technology, which is a big area of investment for us,” said Mr. Ford, who has known Mr. Banga for 20 years.

Mastercard said in September that Mr. Banga, who had been serving as executive chairman, would retire at the end of this year.

Before joining Mastercard, he worked for nearly 13 years at Citigroup Inc., serving in a variety of roles including CEO of Asia Pacific for the bank. He began his career at the Indian subsidiary of Nestlé SA .

Mr. Banga was previously named to the advisory board for BeyondNetZero, a General Atlantic venture that invests in companies developing means to combat climate change, and he will continue in that role.

Based in New York and with offices around the world, General Atlantic specializes in investing in fast-growing companies in the consumer, financial-services, healthcare, life-sciences and technology sectors. The firm was founded in 1980 and manages over $78 billion in assets.

—AnnaMaria Andriotis contributed to this article.

Write to Miriam Gottfried at Miriam.Gottfried@wsj.com