The Conservative peer became ill last month and spent 18 days in intensive care, he confirmed on Twitter.
A spokeswoman said Lord Ashcroft was now recovering in the US and was "out of danger".
The book, Call Me Dave, contains a series of allegations about the prime minister's student days.
It includes claims of drug-taking and a club initiation ceremony, involving a dead pig, that Mr Cameron is said to have taken part in, but the book has been heavily criticised by allies of the prime minister.
Sources have said Mr Cameron was never a member of the club in question, the Piers Gaveston Society, during his time at Oxford University.
Lord Ashcroft suffered septic shock leading to renal and liver failure and heart damage, a report from Channel 5 TV in Belize reported.
The report, which was played to guests at the launch event in London, said he had become unwell in Turkey on 22 September - where he had been visiting war graves to mark the centenary of the Gallipoli campaign - the day after the Daily Mail started serialising the book.
He later flew to Turks and Caicos but his condition deteriorated and on his arrival he was admitted to hospital before being rushed by air ambulance to the Cleveland Clinic in Ohio.
Lord Ashcroft, who grew up in Belize, is said to be recovering in hospital in America.
At the London book launch, a speech was read out on his behalf by publisher Iain Dale.
"As you will have just seen, I have been a little preoccupied for the last four weeks," he said.
"I haven't of course set foot in the UK since my illness but I am reliably informed that my book has caused a bit of a stir."
The former Conservative Party chairman and donor has previously admitted to having personal "beef" with Mr Cameron after not being offered a major job in the coalition government.
In the book, he says Mr Cameron had been aware of his non-domiciled tax status, which was heavily criticised by Labour, in 2009.
But co-author Isabel Oakeshott has insisted the book was not motivated by revenge.
Lord Ashcroft has missed the UK launch party of the controversial book he co-authored about David Cameron, after suffering liver and kidney failure.