Newey moved to Red Bull in 2006, and was instrumental in the titles won with Sebastian Vettel between 2010-2013 and Max Verstappen in recent years.
The Brit's exit comes during a turbulent time at Red Bull, with fractures in the team and controversy surrounding boss Christian Horner.
'Tired' Newey ready to move on
Newey moved to explain his exit during the Miami Grand Prix weekend, which he attended in his usual Red Bull capacity.
"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.