The 75-year-old Harris was a surprise choice to paint the official portrait marking the monarch's 80th birthday next year.
When approached to take the job, he admitted it "frightened the wits out of me" but he said the Queen had made him at ease during two hour-long sittings at Buckingham Palace.
"She was just wonderful. After my initial nervousness she had me totally at ease and it was a delight," said Mr Harris.
The impressionistic image, which will be displayed at the palace's Queen's Gallery, shows the Queen smiling and dressed in a bright turquoise outfit.
Mr Harris revealed he had to work hard to get the image just right, struggling to perfect her dress and teeth.
"It was a bit stressful when I couldn't get the likeness right," he said.
"It looked like a pork butcher from Norwich, it didn't look like the Queen at all.
"Without a good likeness you are dead in the water," he claimed.
But Rolf Harris said he is now thrilled with the result. "I feel it's a good likeness and it shows a relaxation I had not seen in many royal portraits."
"I wanted to avoid that state portrait thing with the jewels and the pomp and splendour - I wanted to capture the lady as she is, with her humanity and reality."
The painting, the Queen's 180th official portrait, took Harris two months to complete after the sittings at Buckingham Palace.