Marshall will leave reigning constructors' champion Red Bull at the end of the 2023 season, although he steps back from his current role with immediate effect, to bring his 17-year stint in Milton Keynes to an end.
In January of 2024, Marshall, a former Renault designer who is credited with evolving the team's innovative mass damper system that helped it to the 2005 and 2006 constructors' titles, will take up the post of technical director at McLaren.
The Briton served as chief designer at Red Bull throughout its 2010-2013 championship-winning pomp before taking a wider role in the specially-created position of chief engineering officer.
More recently, this meant he was heavily involved in the fledgling Red Bull Powertrains project.
McLaren team principal Andrea Stella said of the marquee signing: "I am incredibly pleased that Rob will be joining McLaren. With over 25 years working in motorsport, Rob comes to us with a wealth of expertise and experience, elevated by his tenure and track record at Red Bull Racing.
"Rob's appointment is one of the fundamental steps and a natural fit to aid the team's journey to get back to our winning ways."
Since Stella was called up by McLaren Racing CEO Zak Brown to replace Sauber-bound Andreas Seidl at the helm of the F1 team, the Italian has conducted a major review of the leadership structure at Woking over the winter.
This has led to him appointing Indianapolis 500 winner Gil de Ferran as a non-executive advisor as well as ousting technical director James Key.
As part of a revised management trio, McLaren lured Ferrari's head of vehicle concept David Sanchez.
Stella continued: "We are a team with the ambition of fighting for championships, but over the last couple of seasons we have not shown a steady upward trend from an on-track competitiveness point of view. Over the last few months, we have worked towards inverting this trend.
"The approach we have adopted is comprehensive and is based on strengthening the Team from a people and expertise point of view, along with the ongoing projects to upgrade technology and infrastructure that will shortly come to fruition.
Completing the senior technical revamp, Neil Houldey will serve under Marshall in the newly-created role of deputy technical director for engineering and design.
Red Bull team principal Christian Horner said: "We would like to thank Rob for everything he has done for the team over the past 17 years.
"His work on the generation of cars that gave us four incredible championship doubles between 2010 and 2013 was truly outstanding.
"In the years since he has continued to be a key figure at the team and in 2016 took on the broader role of Chief Engineering Officer which has seen him involved in other projects across the business.
"His influence will be missed but once again we thank him for all he has done and wish him the very best in his new role."
