The Dutch teenager, son of ex-F1 driver Jos Verstappen, will partner Daniil Kvyat in the Red Bull feeder team with Frenchman Jean-Eric Vergne surplus to requirements.
"Ever since I was seven years old, Formula One has been my career goal, so this opportunity is truly a dream come true," Verstappen said on the team's website.
Verstappen, who turns 17 next month, will beat the age record currently held by Spain's Jaime Alguersuari, who was 19 years and 125 days when he made his debut in 1990.
"We've all worked tremendously hard to reach Formula One and I will give my absolute best to be successful in the pinnacle of motorsport," he said, thanking his father for his support.
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"With the return of the Verstappen name to Formula One, I hope we can relive old memories and I'm hoping to see many fans at all the Grand Prix circuits."
Verstappen is following the path of four-time world champion Sebastian Vettel and Red Bull team-mate Daniel Ricciardo, who were also members of the Red Bull Junior Team.
"We consider Max to be as one of the most skilled young drivers of the new generation and we believe he has the necessary maturity and mental strength to take on this challenge successfully," he said.