Red Bull said Fallows, who left the team last year after working as aerodynamics team leader, had returned and was starting his new job with immediate effect.
McLaren announced last October they had signed Prodromou but Red Bull, contructors' champions for the past four years, were determined to hold the much sought-after Briton to his contract.
They did not say when his leave would formally end.
Prodromou was McLaren's head of aerodynamics until 2006, having joined that team in 1991, when he followed Adrian Newey to Red Bull.
- Sports & Recreation
- Red Bull