The team, who last won a race in 2012, have been using the Toyota facility in Cologne, Germany, for most of the past decade.
"The 1.5 seconds we are missing to the top cars or even more depending on the race track is simply aero load," newly-appointed team principal Andreas Seidl told reporters at the French Grand Prix.
"One of the big deficits we have clearly is not running our own wind tunnel," he added. "So we're very happy that the decision has been made that we install a new wind tunnel in Woking.
"It is obviously a great message for everyone inside the team because it also shows how serious (McLaren Racing chief executive) Zak (Brown) and the shareholders are regarding our way back to the front.
Construction of the facility, replacing an old one, will take about two years and will be shared with the automotive side of the company and other motorsport projects.
McLaren enjoyed their best qualifying session since 2016 at the French Grand Prix on Saturday, with British rookie Lando Norris lining up in fifth place and Spaniard Carlos Sainz sixth on the grid.
The team are currently fourth in the standings, two points ahead of engine providers Renault's factory team.
(Reporting by Alan Baldwin, editing by Nick Mulvenney)
