Barber was named as the winner of the £10,000 award, which rewards debuts, at an awards ceremony held this evening (27th June) at Fortnum & Mason in London.
Her book, which was previously long-listed for the Women's Prize for Fiction, revolves around the question of authorship of Shakespeare's plays, and the mysterious murder of his contemporary Christopher Marlowe.
The chair of the judges Joanne Harris said: "Barber's novel stood out from the shortlist because it is a unique historical conspiracy story that engages all the senses. It is an enticing as a top-flight thriller, with the welcome addition of gorgeous, evocative language as visual and concise as a screenplay."
The Marlowe Papers was chosen ahead of the two other shortlisted novels, Jenni Fagan's The Panopticon (William Heinemann) and Gavin Extence's The Universe Versus Alex Woods (Hodder & Stoughton).
Miriam Robinson, head of marketing at Foyles and also on the judging panel, commented: "Literary prizes are in many ways comparable to the role of the bookseller who, in offering enthusiastic and wholehearted recommendation for a title, can change its prospects within an incredibly crowded market."
The Desmond Elliot Prize, founded in the memory of publisher and literary agent Desmond Elliott, is now in its sixth year. The previous winners are Grace McCleen, Anjali Joseph, Ali Shaw, Edward Hogan and Nikita Lalwani.