Dame Anna will remain in charge of Vogue globally and as chief content officer of the media company Conde Nast, which oversees prominent media brands including Vogue, Vanity Fair and GQ.
Malle, the daughter of actress Candice Bergen and French film director Louis Malle, will take on her new role immediately, the magazine said.
She was previously the editor of Vogue.com and co-host of The Run-Through, Vogue's weekly fashion and culture podcast.
She will now lead the creative and editorial direction of the title and join Vogue's ten existing heads of editorial content around the world, reporting to Dame Anna.
Malle said: "Fashion and media are both evolving at breakneck speed, and I am so thrilled - and awed - to be part of that.
"I also feel incredibly fortunate to still have Anna just down the hall as my mentor."
Announcing the appointment, Dame Anna said: "Fashion is the art of embracing change, but some changes run closer to one's heart than the rest.
"When it came to hiring someone to edit American Vogue, letting me turn my attention more intensely to Vogue's multifaceted growth across its global audiences and publications and events like the Met Gala and Vogue World, I knew I had one chance to get it right.
"I'm thrilled to announce that Chloe Malle will be the next head of editorial content for our US title, leading the American magazine and guiding its digital coverage.
"She's a voracious, engaged journalist with an intuition for women's changing interests now - and her eye for the definitive image is exceptional.
"Chloe has long been one of Vogue's secret weapons when it comes to tracking fashion. But she is not so buried in the industry that she misses the world: like the best designers, she understands fashion's big picture, its role shaping not just what's on the runway but the changing fabric of modern life.
"Although she is no stranger to the glamour of red carpets, her talent has been for original thinking and hard work."
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