The former prime minister recalled a series of conversations with the late monarch during his time in office as the first anniversary of her death approaches next week.
“It was because of her humanity and sympathy that you felt, as PM, that you could really open up to her, tell her absolutely everything,” he said.
“I once told her that I had a nightmare that I had been late for her and the duke (of Edinburgh).
“‘Oh yes’, she beamed, and I could tell that she had heard this one before, probably from other PMs. ‘Were you naked?’ she asked, because it turns out that is a common feature of such dreams.”
The late Queen also allowed him to exercise in Buckingham Palace gardens after he fell ill and was the first to tell him one of the UK’s F-35 fighter jets had blown a gasket and fallen into the Mediterranean Sea, he said.
“If she was surprised by my ignorance, she didn’t let it show. She was never less than supportive, and always encouraging, always thinking about how others might be feeling,” Mr Johnson said.
The column is his first journalistic job since quitting Parliament earlier this year after being found to have lied to MPs about his knowledge of partygate.