It was widely reported last week that the 65-year-old, regarded as the greatest designer in the sport's history, was set to quit following a controversy involving allegations about team principal Christian Horner.
The British-based Red Bull team have won six constructors' titles and seven drivers' titles, split between Sebastian Vettel and Max Verstappen, with Newey-designed cars to date.
They are on course to do the double again in 2024, with Dutch driver Verstappen the dominant force in the sport.
Ferrari, soon to be joined by Lewis Hamilton, appear to be in pole position to sign up Newey.
The British designer, a chief architect of Red Bull's dominance, is set to end his stay in the "first quarter" of next year, according to a statement from the team.
"Ever since I was a young boy, I wanted to be a designer of fast cars. My dream was to be an engineer in Formula One, and I've been lucky enough to make that dream a reality," Newey said.
"For almost two decades it has been my great honour to have played a key role in Red Bull Racing's progress from upstart newcomer to multiple title-winning team."
Horner lavished praise on Newey, saying "all of our greatest moments from the past 20 years have come with Adrian's hand on the technical tiller".
"His vision and brilliance have helped us to 13 titles in 20 seasons," he said.
"His exceptional ability to conceptualise beyond F1 and bring wider inspiration to bear on the design of Grand Prix cars, his remarkable talent for embracing change and finding the most rewarding areas of the rules to focus on, and his relentless will to win have helped Red Bull Racing to become a greater force than I think even the late (founder) Dietrich Mateschitz might have imagined."
Red Bull said Newey would step back from design duties to focus on final development and delivery of Red Bull's first hypercar, the RB17.
'Called the shots'
He will continue to attend specific races to support the team until the end of the current season.
Newey, expected to be in Miami for this weekend's race, has also worked with championship-winning teams at Williams and McLaren in his long career.
It was reported that he became unsettled after Horner was accused of sexual harassment and inappropriate behaviour by a female employee.
The team principal was cleared in February of wrongdoing by an internal investigation carried out by Red Bull's parent company before the employee was then suspended. She is appealing that decision.
Former Formula One supremo Bernie Ecclestone told AFP that Newey's legacy to the team would take a while to assess.
"Teams have been trying to poach him for a long time," Ecclestone, 93, told AFP by phone in Portugal.
"After the recent events at Red Bull he probably thought 'it may be best I leave now'.
"I have not spoken to him since it happened.
"Let us wait and see legacy wise.
"I think obviously he has been around a long time, the good thing about him is he was not a dreamer, he called the shots as they were.
"How much contribution he made to the success we have to wait and see."
Verstappen's Red Bull future was thrown into doubt last month after his father, Jos, said the team was in danger of being "torn apart" if Horner remained in his job.
Last year, Verstappen and Red Bull produced the most dominant season in F1 history, with the Dutchman winning 19 of the 22 races and the team all but one.
Verstappen has won four of the first five races in 2024.
