US Edition The Australian artist, who was made a CBE in the Queen's birthday honours list in 2006 for his services to entertainment and the arts, was asked to commemorate the monarch's 80th birthday on canvas at Buckingham Palace.
"I was as nervous as anything. I was in a panic," he told the Daily Telegraph of the day the Queen sat for him.
"We sat down and I said: 'What are you like with the smell of turpentine? Does that affect you badly?'
"She said: 'We shall find out, shan't we?' So I said: '...Because I like to slosh on paint to kill the white of the canvas with a bit of turpentine. Then I start with a blur which looks something like the subject and I gradually refine it.'
"And she said: 'Sounds very strange to me.'"
While he continued painting, the conversation turned to the Queen's Coronation, which Mr Harris, 78, had attended.
By the end of the portrait sitting, he said, the atmosphere had become more relaxed. "She put us all at our ease," he said.
"We finished up chatting like very old friends. She was just lovely through the whole thing."
Mr Harris chose a soft emerald glow and relaxed pose for his portrait of the Queen, which was commissioned to mark her 80th birthday and was later voted the public's second favourite portrait of her.
His popularity was underlined by a poll published in the Daily Telegraph today in which Mr Harris beats the nation's richest living artist, Damien Hirst.
The survey, "What the British really think about art today", was conducted by leading publishers Dorling Kindersley to coincide with a 540-page guide to artists and paintings titled "Art: The Definitive Visual Guide".
The street artist Banksy was voted the nation's favourite British artist, ahead of JMW Turner, David Hockney, John Constable, LS Lowry and Henry Moore.
In the broader category of overall favourite artist, Rolf Harris and Damien Hirst were beaten by artists Van Gogh, Picasso and Andy Warhol.
The Mexican painter Frida Kahlo was voted favourite female artist, with English sculptor Dame Barbara Hepworth coming second.
The nation's favourite paintings were: The Water-Lily Pond (Monet), Guernica (Picasso), The Scream (Munch), Girl with a Pearl Earring (Vermeer) and Sunflowers (Van Gogh).
Mr Harris, who presented the BBC TV shows Star Portraits with Rolf Harris and Rolf on Art, said he was "thrilled to bits" by the news.
He said: "It's possibly because television is a fantastic medium for publicity.
"People can see you on TV sloshing paint around with big, four-inch brushes and I learned to talk to camera in a friendly voice, not talking down to people, just explaining what I was doing. People like Picasso, Van Gogh and Rembrandt did not have a weekly TV programme where people could see them painting."
- Art: The Definitive Visual Guide (Dorling Kindersley, RRP £30) is available from the Telegraph Bookshop for £27 + £1.25 p&p. Call 0870 428 4112 or go to books.telegraph.co.uk