The Franco-German will effectively step into the role that Tim Goss held until the end of last year, prior to his departure from the governing body as he moves to the RB squad.
Monchaux will report directly to the FIA’s long-serving single-seater director Nikolas Tombazis, who has been with the organisation since 2018.
He will be tasked with similar responsibilities to Goss and will play a key role in the formulation of the new 2026 F1 rules that will be pulled into shape over the course of this year.
Monchaux has a long career in F1, having originally started in 2002 with Toyota, where he served as aerodynamics leader until the Japanese manufacturer left F1 at the end of 2009.
He switched to the Ferrari team, also working in its aerodynamics department, for the following season and remained there until the end of 2012.
After a period away from F1, where he worked at Audi from 2013, he returned to grand prix racing in 2018, joining Sauber as its new head of aerodynamics.
He was then promoted to become Sauber technical director in 2019 following the departure of Simone Resta, before he left the squad last year following the signing of James Key.
Monchaux’s appointment comes against the backdrop of the FIA having lost several senior figures over the winter, including Goss and its sporting director Steve Nielsen.
Earlier this year, the FIA announced that Nielsen would be replaced by Tim Malyon, who previously served as safety director.
The FIA says that Malyon "will oversee all sporting matters, including race direction and the Remote Operations Centre in Geneva," with Niels Wittich remaining in his role as race director.
The shake-up within the governing body had prompted some concern from senior F1 team figures, with Mercedes boss Toto Wolff hoping that the FIA could find greater stability in the future.
"It's concerning to see so many good people leaving," Wolff said. "Losing Steve Nielsen is a big blow. I couldn't think of a more knowledgeable and fair sporting director. "As a leader, it's about the culture and environment you create for people to thrive. When people as competent as these leave an organisation, there is a vacuum. That's clear. And you've got to ask yourself: why is it suddenly that so many people have decided to call it a day?
"What [the FIA] needs is stability. The FIA is one of three key stakeholders of the sport [along with FOM and the teams].”