Prodromou worked for the Woking team before joining the current world champions in 2006 to work under fabled chief technical officer Adrian Newey.
It is unlikely that Prodromou will work for McLaren until their partnership with Honda is renewed in 2015.
"We do have to remember that the contract Peter has at the moment is a Red Bull contract and I have to respect that. It's for them to talk about what his terms are and what his leave dates are," Sky Sports News quotes McLaren's managing director Jonathan Neale as saying.
"But in terms of our position then, yes, we have recruited Peter. We're really excited about him joining the team."
Red Bull secured a one-two qualifying at Suzuka earlier today, with Mark Webber pulling off a surprise by ousting teammate Sebastian Vettel, who is on the verge of a fourth straight world championship.