The 22-year-old Dutchman has been with the team since being promoted from Toro Rosso part-way through the 2016 season.
“Red Bull believed in me and gave me the opportunity to start in Formula 1 which I have always been very grateful for,” said Verstappen.
“I want to win with Red Bull and our goal is of course to fight for a World Championship together.”
Verstappen became the youngest winner in F1 history when he won the Spanish Grand Prix as an 18-year-old in 2016.
He finished third in the title race behind champion Lewis Hamilton and Valtteri Bottas last season and the new deal appears to end speculation about the possibility of Verstappen moving to Mercedes or Ferrari.
“With the challenge of the 2021 regulation changes on the horizon continuity in as many areas as possible is key,” said Red Bull team principal Christian Horner.
“Max has proven what an asset he is to the team, he truly believes in the partnership we have forged with our engine supplier Honda, and we are delighted to have extended our relationship with him.”