Sir Sean Connery's appearance at the festival has sold out
Organisers said they were experiencing an unprecedented demand for tickets for book festival events.
Its website had more than 300,000 hits in its first hour and phone lines took more than 21,000 calls.
Other events which have already sold out include former MP Tony Benn and the BBC journalist Alan Johnston.
Festival dates including Margaret Atwood, Jonathan Dimbleby and Scotland's First Minster Alex Salmond have also sold out.
Sir Sean, who appeared at the opening night of the Edinburgh Film Festival on Wednesday with his arm in a sling, will appear at the book festival on 25 August.