Newey joined Red Bull as chief technical officer in 2006, having previously designed world championship-winning grand prix cars for Williams and McLaren in the 1990s.
Sebastian Vettel's three straight drivers' world championship crowns since 2010 have all come in Newey machines while Red Bull has also won the constructors' title in each of those seasons.
Webber, who has taken each of his nine grand prix wins in Newey-influenced machinery, said that his ability to remain focused on performance while most of the sport becomes embroiled in politics has been key in the team's surge forwards.
Webber said: "We need, behind all the smoke and mirrors of a Formula 1 team, to make a racing car as quick as possible to do the business in qualifying and the races.
"Adrian never loses sight of that and he's a huge influence.
"You have him beating the drum and generally being a big beacon for the team here in terms of design and philosophy of where the car needs to be. You need that to be successful here.
"And when you start getting some success as well things change so quickly. Things becomes much easier."
Webber and Vettel remain team-mates for 2013 after spending the past four years together at Red Bull.
The team has yet to announce a launch date for its 2013 challenger.