The shoot, by photographer Josh Olins and set in Norfolk's English countryside, features Kate in "casual clothes rather than adopting a more formal approach," the magazine said in a statement.
Two of Olins' portraits will be on display at the gallery, in the Vogue 100: A Century of Style exhibit, beginning Sunday. Kate, 34, has been the patron of the gallery since 2012, soon after her wedding to Prince William.
"Josh has captured the Duchess exactly as she is – full of life, with a great sense of humor, thoughtful and intelligent, and in fact, very beautiful," Nicholas Cullinan, director of the National Portrait Gallery, said in a press release.
British Vogue's editor-in-chief, Alexandra Shulman, said this project had been one of her "greatest ambitions for the magazine."
"I'm delighted the Duchess agreed to work with us and the National Portrait Gallery, and as a result of this unique collaboration we have a true celebration of our centenary as well as a fitting tribute to a young woman whose interest in both photography and the countryside is well known," Shulman said in the release.
Kate shared that delight, a spokesperson said in the release: "The Duchess was delighted to play a part in celebrating the centenary of an institution that has given a platform to some of the most renowned photographers in this country's history.
"She is incredibly grateful to the team at Vogue and at the National Portrait Gallery for asking her to take part. She would like to thank Josh Olins for being such a pleasure to work with. The Duchess had never taken part in a photography shoot like this before."
The full shoot will also be available in June's centenary issue of British Vogue, on sale Thursday, May 5.