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Ghanaian-born Enninful is the successor to Alexandra Shulman, who announced in January she would be stepping down from the magazine after 25 years in charge.
Enninful, 45, joins from W magazine, where he has been fashion and creative director since 2011. Previously, he had also worked for the Italian and American versions of Vogue.
Jonathan Newhouse, chairman and chief executive at Condé Nast International, the magazine's publisher, said Enninful was "an influential figure in the communities of fashion, Hollywood and music" who was "supremely prepared" for the job.