The former prime minister made the revelations to the Chris Evans Radio Show, as his memoir For the Record, was launched yesterday.
When requested if it was true that President Obama had tucked him up in mattress, Mr Cameron replied: ‘Yes he did. I promise it’s a true story.
‘I went to see him in 2012, he took me off to a basketball game in Ohio and we’re flying again on Air Force One.
‘And of course at that time of night it’s late in America. But it was like 4:00 in the morning in the UK.
‘And he said David, you look a bit tired why don’t you go and sleep on my mattress.
‘And I mentioned, nicely thanks very a lot and so he took me up to the kind of nostril cone of Air Force One.
‘There was a blanket with the White House crest on it and I lay on the bed. He said I’ll put the blanket over you and as he was tucking me in, he mentioned I guess, you already know, Roosevelt by no means did this for Churchill.
‘So who says the special relationship isn’t going robust? But we acquired on very nicely. I preferred him, he was extraordinarily good.’
Mr Cameron additionally retold the story of how the KGB had tried to recruit him, whereas he was on a niche yr vacation in Russia, earlier than going up to Oxford college.
During a visit to the Black Sea with a faculty good friend, Mr Cameron mentioned a ‘couple of Russians who spoke perfect English’ befriended them took them out for lunch and dinner.
He mentioned they requested them what they thought of Western democracy in the UK and what their views have been on Russia.
Mr Cameron added: ‘And we have been a bit suspicious at the time, once I acquired to college I had talked to one or two individuals about it.
‘They mentioned it was in all probability an try to discover out who you have been and faucet you up.
‘But I promise I haven’t been a Soviet spy all this time. But so it actually did occur.’
Mr Cameron additionally justified writing his memoir, saying he thought that at some stage prime ministers had to write one.
The previous Etonian additionally mentioned he hoped he wouldn’t be a persistent kind of commentator on the whole lot that’s occurring, ‘because I think ex prime ministers do have some interesting perspectives perhaps, particularly on foreign affairs because we spent so much time dealing with them in office’.