Banga, who took charge of the company just after the 2008-09 financial crisis, has seen the payment processor's revenue triple during his tenure as online shopping gained prominence around the world.
India-born Banga will take on the role of executive chairman, while Miebach will become the company's president on March 1.
Chairman Richard Haythornthwaite will retire after more than a decade when Banga assumes his new role, the company said in a statement.
Before joining Mastercard as president of Middle East and Africa in 2010, Miebach served as managing director at Barclays Bank and general manager at Citibank.
In connection with Miebach's appointment as president, Mastercard has entered into a new compensation agreement that adds $750,000 to his annual base salary, the payment processor said in a filing.
Miebach will also receive an equity grant with a target value of $6.25 million. His compensation as chief executive officer will be determined later, the company added.
Mastercard on Monday warned its first-quarter net revenue would take a hit if coronavirus outbreak persists through the quarter.
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