The pair - regarded as two of the greatest British artists of the 20th century - were friends for decades but Hockney only sat for Freud in 2002 and the painting has not been seen in public since a show at the National Portrait Gallery in 2012.
Tom Eddison, director of contemporary art at Sotheby’s London, said it was hard to think of two British artists “who are as both critically and commercially acclaimed”.
“In this magnificent portrait we bear witness, not only to the enduring relationship of these two eminent masters but, moreover to, a tour-de-force of portraiture,” Eddison said.
“Quite simply, his portrait of David Hockney is a masterpiece - a sublime testament to the measure of Freud’s uncompromising scrutiny and ability to capture the mood and the inner essence of his sitters.”
The two men first met in 1962, when Freud was almost 80 and Hockney 65, and spent hundreds of hours at Freud’s west London flat as he painted.
His daughter Bella Freud said it was like seeing “two cool older boys at school who were engrossed in each other’s conversation.”
The painting is going under the hammer at Sotheby’s modern and contemporary sale on June 29.