Machin worked on wind tunnel development through Renault-powered Red Bull's four successive world championships from 2010 to 2013, having joined that team's predecessor Jaguar in 2002.
"It is clear that Renault Sport is serious about mounting a fresh challenge within F1 and I am happy to join the team," he said in a team statement.
Formula One is going through a major rule change this season, with wider tyres and revised aerodynamics that will see the cars generating much more downforce and cornering faster than before.
"The latest generation of regulations are, if anything, more aero-crucial than before so to have Pete join us at such a time of exciting evolution will be of the greatest benefit," said Renault Sport Racing managing director Cyril Abiteboul.
Former champions Renault, who bought the failing Lotus team at the end of 2015 to return as full constructors rather than simple suppliers of engines, finished ninth of 11 teams last season.
Red Bull's Renault power units now carry Tag Heuer branding.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
