The app has over 36m subscribers and promotes mostly African artists.
The deal gives Downtown the rights to over 700 compositions, including songs by One Direction, Sam Smith and Madonna.
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The label is now worth over $300m, with Swift's masters accounting for 35% of the company's market share.
"Vikram’s experience as a global industry leader made him the ideal candidate".
David Cobb, Cece Winans and Ben Vaughn will also serve on Studio Bank advisory board.