In a statement from London released Thursday, Burton said she intends "to stay true to his legacy" by turning out "modern beautifully crafted clothes."
McQueen was hailed as a creative genius in the fashion world. He committed suicide in his London apartment in February.
Burton joined McQueen's company in 1996, a year before graduating Central Saint Martins College of Art and Design. She most recently served as head of design for womenswear.
Parent company Gucci Group said that because Burton worked so closely with McQueen she has "the vision necessary to take it forward."
Burton will oversee women's and men's apparel as well as accessories.
