Newey moved to Red Bull in 2006, and was instrumental in the titles won with Sebastian Vettel between 2010-2013 and Max Verstappen in more recent years.
"Formula 1 is all-consuming and I've been at it for a long time now," Newey told Sky Sports F1.
"2021 was a really busy year because of the tight battle with Mercedes through the championship, and at the same time putting all the research and development into the RB18 which is the father of this generation of cars.
"I don't know, there comes a point where I just felt, as Forrest Gump said, 'I'm feeling a little bit tired'."
Newey will leave Red Bull in the first quarter of 2025. His future beyond that is yet to be decided, though he did rule out a switch to Aston Martin.