The former world champions, who are struggling with Honda engine reliability and performance issues this season, said the winner would be offered a one-year contract to help them improve the car.
With real track testing heavily restricted under the regulations, Formula One teams use simulators to acquire data and develop their cars. The duties are often handed to the official reserves.
McLaren Technology Group Executive Director Zak Brown said in a statement that it was the right time to connect the worlds of racing and gaming in a new way.
"The winner will genuinely be a key part of our team at McLaren," he added. "This is for real: we absolutely require additional support across our two simulator platforms."
The 'World's Fastest Gamer' competition will be a collaboration between McLaren, team sponsor Logitech G and Darren Cox, the founder of virtual motorsport's GT Academy.
McLaren said the initiative would make them the first Formula One team to enter the E-sports arena.
Six international finalists will be selected by experts in gaming and Formula One with a further four finalists chosen from qualifying events online.
McLaren said contestants would race across a variety of different gaming titles and platforms and would also need to demonstrate engineering know-how, teamwork and the necessary mental and physical strengths.
The world of E-sports is enjoying huge growth with traditional media companies and big videogame publishers clamouring to get involved.
Formula One's owners Liberty Media, who took control of the sport in January, have highlighted gaming as a growth area as they seek new audiences and increased revenues from North America.
"Less than one percent of revenues are from digital," Liberty Media chief executive Greg Maffei said last year. "I think there's a lot of things that can be done around gaming, VR (virtual reality) and AR (augmented reality)."
The global E-sports audience is expected to reach 385 million this year with the market generating $696 million (£538.8 million), according to research firm Newzoo.
North America is the largest market, with predicted revenues of $257 million in 2017 and $607 million by 2020.
The all-electric Formula E series staged a virtual race between all of its drivers and gamers in Las Vegas last January. The winner, Dutch virtual racer Bono Huis, collected a $200,000 jackpot.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
