Enninful will oversee all editorial content and will report to Albert Read, managing director of Condé Nast Britain.
Enninful has been creative and fashion director of W Magazine since 2011. He was the fashion director of I-D magazine and contributed to American Vogue and Italian Vogue. He was bestowed an OBE (Officer of the Most Excellent Order of the British Empire) last year, and in 2014 was awarded fashion creator of the year by the British Fashion Council.
Shulman led British Vogue for 25 years and was the longest-serving editor at the magazine.
"By virtue of his talent and experience, Edward is supremely prepared to assume the responsibility of British Vogue," Newhouse said in a statement, calling Enninful "an influential figure in the communities of fashion, Hollywood and music which shape the cultural zeitgeist."