The former Tory leader hailed her wisdom and said she was like a grandmother he could confide in.
He said she had been on sparkling form during their last meeting, despite reportedly suffering from a form of cancer before she died aged 96 in September 2022, two days after he quit as PM.
Mr Johnson told today's Rosebud with Gyles Brandreth podcast: "Her late Majesty the Queen was the most phenomenal fund of wisdom and knowledge...very wise.
"I always felt buoyed and bucked in her presence. You could not help feeling the cares lift when you went into her room. And it all seemed much easier and more bearable.
"Because she'd seen it all before.
And there was nothing you could tell her that would shock her.
"I mean, she was like having tea with your favourite grandmother and telling her things that you wouldn't dream of telling your parents."
Mr Brandreth, 76, a close friend of the monarch and Prince Philip, revealed in his biography Elizabeth: An Intimate Portrait, published three months after her death, that he had heard she had a form of myeloma.
He wrote that the diagnosis "would explain her tiredness and weight loss and those 'mobility issues' we were often told about during the last year or so of her life".
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