The artist, who is described by the paper as a "Yorkshire-born working class genius" and a "lifelong Sun reader", has hand drawn rays of sunshine radiating from the top-left hand corner of the masthead.
The one-off Hockney redesign will appear on tomorrow's front page, with an in-depth interview inside the paper, to coincide with the 80-year-old artist’s exhibition at the Tate Britain gallery, which opens next week.
Hockney came up with idea several years ago when a number of artists were asked to redesign a classic British logo.
The Sun heard Hockney had picked the paper and asked the artist if it could reproduce his design but he initially declined.
The tabloid approached him again more recently when plans emerged about his exhibition and he agreed for his design to be used in the paper.
Hockney said: "I was delighted to be asked. Once I thought about the idea it didn’t take me long. The sun and The Sun. I love it."
Tony Gallagher, editor-in-chief of The Sun said: "Nothing demonstrates the enduring position of The Sun in British culture like having Britain’s most-loved living artist redesign our logo."
Hockney may be a keen newspaper reader but in 2012 he predicted traditional mass media was "dying" because of new technology.
"The power of the old media barons is in decline – I am sure Rupert Murdoch knows this – and seems to be passing to the masses themselves, whether they want it or not," he wrote in an article for the Financial Times.