She is the only daughter of the second Viscount Norwich and his first wife, Anne (née Clifford), and a granddaughter of Lady Diana Cooper. She has a brother, the Hon. Jason Charles Duff Bede Cooper, and a half-sister, Allegra Huston, the only child of Lord Norwich and Enrica Soma Huston, the estranged wife of American film director John Huston. She attended the French Lycee, the Convent of the Sacred Heart in Woldingham and Camden School for Girls. She then went to St Hugh's College, Oxford and obtained a degree in English language and literature. In July 2015, she was awarded an honorary doctorate from the University of York.

She spent time in Alexandria, Egypt, with Voluntary Service Overseas teaching English at the University of Alexandria. She has also lived in America, mostly in New Mexico.

In 1986, Artemis Cooper married fellow writer and historian Antony Beevor. The couple have two children, Nella and Adam.