Puig will supervise Honda's Asia Talent Cup and its recruitment of young riders, meaning he will end his direct relationship with Pedrosa after overseeing his whole MotoGP career so far.
Honda Racing Corporation chief Shuhei Nakamoto said: "We are very happy to increase Alberto's role in HRC and make use of his extensive knowledge in this world.
"He is a valuable asset to Honda Racing and we must utilise him and benefit from his wealth of experience."
Pedrosa said it was the right time to change his relationship with Puig.
"After many years working together on track with Alberto, next season he will not be by my side in the garage," said Pedrosa.
"He will be taking care of new projects and I feel that he has already given me so much that now it is time to change our relationship slightly.
"Anyway, I know that Alberto will be there for me if I need something, and this is the most important thing."
Puig had a riding career of his own before switching to management, racing for Pons in the 500cc world championship from 1993-7 and winning the '95 Spanish Grand Prix.