The £10,000 prize recognises first-time novelists in the UK and Ireland.
Cleave’s fellow judges are Patrick Neale, president of the Booksellers Association, and Isabel Berwick, associate editor of the Financial Times "Life & Arts" section.
Cleave, the latest in a line of notable writers to head up the panel, said: “The Desmond Elliott Prize has proved itself a serious and consistent award for the very best debuts in fiction. As British and Irish writing is in such first-rate health, I am expecting the reading to be exciting and the judging difficult. I’m delighted to be involved.”
The judges are said to be looking for novels that have a compelling narrative and arresting characters, and are vividly written and confidently realised. Last year's winner was Ros Barber, for her novel in verse, The Marlowe Papers (Sceptre).
Now in its seventh year, the award is presented in the name of the late publisher and literary agent Desmond Elliott.
A longlist of 10 books will be announced in April 2014 and a shortlist in May. The winner will be revealed on 3rd July 2014 at a ceremony at Fortnum & Mason.