The former Toro Rosso driver will serve as back-up to triple world champion Sebastian Vettel and team-mate Mark Webber for a second consecutive year, as well as play an important role in development.
Buemi said: "I know everyone at Red Bull Racing well and it's good to remain with the team for another year.
"Of course my aim is to be driving at the races again, but I am still learning all the time from my work with the team."
Appreciating the valuable role played by Buemi, team principal Christian Horner said: "Sebastien joined the Red Bull junior team in 2004, has worked with Red Bull Racing in 2008 and 2012 and has significant race experience.
"He is an integral member of the team and will complete important simulation work for us throughout the year."