The book will be called The Maintenance Memoirs and will be written by Cleese and a professional biographer.
It should be able to command an advance of around £2 million from potential publishers.
Cleese told The Sun: "I don't think anybody's ever done one like this. I'd been putting it off - partly because I was too busy, and also because it was too difficult trying to remember things."
The 71-year-old has previously said that he needs to earn around £1 million a year for the pay-off settlement, and claims that the divorce has cost him $65 million (£40m). He admits to having been "naive" about divorce beforehand.
Eichelberger, who was married to Cleese for 19 years, was the Monty Python actor's third wife. He was previously married to Connie Booth and Barbara Trentham.