The challenge will start on 8 August and continue until they reach the end of the report into the Iraq war.
At a rate of about 120 words per minute, the reading is predicted to take more than two weeks to complete.
Members of the public have also been invited to sign up.
Sir John Chilcot's report, published earlier this month, said former Prime Minister Tony Blair had overstated the threat posed by Saddam Hussein, sent ill-prepared troops into battle and had "wholly inadequate" plans for the aftermath of the invasion of Iraq in 2003.
The Iraq Out & Loud event is being organised by Fringe veterans Bob Slayer and Omid Djalili, and will be held in a garden shed, beside Bob Slayer's Blundabus on South College Street, with two readers each hour.
Mr Slayer said: "Producing this is going to be a truly mammoth undertaking, however I know I would totally regret not doing it much more than actually doing it."
Tickets to be part of the small live audience in the shed go on sale on Monday, with four seats allocated per hour.
Crime writer Ian Rankin, SNP MP Tommy Sheppard and comedians Stewart Lee, Reg D Hunter and Arthur Smith are among the names who have already agreed to take part.
Mr Rankin said: "I was on my holidays when the Chilcot Report was published, so this is my best chance to get to read at least some of it. It's either that or wait for the film."
A host of comedians, writers, and politicians are to stage a non-stop, live streamed reading of the Chilcot Report in its 2.6 million word entirety as part of an Edinburgh Fringe show.