Enninful, a close friend of British supermodel Naomi Campbell, will replace Alexandra Shulman, who is stepping down on August 1 after more than 25 years.
He was born in Ghana, brought to London as a child and was scouted as a male model aged 16 before becoming the youngest editor in the industry when he was named fashion director of i-D magazine in 1991 aged just 18.
Enninful has already worked at Vogue's Italian and US editions and has been the creative and fashion director of the US style magazine W since 2011.
Enninful was named fashion creator of the year by the British Fashion Council in 2014 and last year, he received an honour from Queen Elizabeth II.