The former Prime Minister described Mr Johnson’s time as mayor as “dysfunctional” - and said he could have done the job “a lot better”.
He also recalled a time the current PM told him he had a “nine-point plan” for an idea - but “couldn’t even remember the points”.
Mr Cameron made the claims in his new autobiography, ‘For The Record’, his anticipated tell-all memoirs from his time in Government.
In the book, which he wrote at home in Oxfordshire, Cameron addresses a host of issues such as his feelings on Brexit, his family and his relationships with other senior Tory figures.
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Speaking of Mr Johnson, he wrote: “As for the London mayoral election, there was a widespread theory that I didn’t want Boris to win a second term - that we were such great rivals that I would rather see the capital go to Labour than my old rival triumph.
“It really wasn’t like that. Boris was the one who was full of jealousies and paranoias, which so often influenced his behaviour. I wanted him to win.
“He had been a great mayor, but I felt city hall was dysfunctional, and that he could do the job a lot better.
“I had been advising him to pick winnable fights with the government on things he controlled and that we could try to accommodate - like transport - rather than economic policy, which wouldn’t change and which would leave us both coming off badly.”
The attack follows a number of other scathing assessments of Mr Johnson’s character which have emerged during his time in office.
Sir John Major compared the Prime Minister to a “dishonest estate agent” over his prorogation of Parliament.
He was called the "father of lies" at the Supreme Court during a hearing over the legality of his Commons suspension.
Mr Johnson has also been accosted by angry members of the public.
On Wednesday, he was confronted by the father of a sick girl over the current state of the NHS when the Prime Minister visited a hospital.
Omar Salem told Mr Johnson his newborn daughter had to wait two hours for treatment in the children’s ward at Whipps Cross University Hospital, in east London, after she nearly died on Tuesday.