The agreement means that the Dutchman, who only graduated from karts this year, will become the youngest driver in Formula 1 history when he debuts in 2015.
His performances in the European F3 Championship helped him earn a place on Red Bull's junior programme, and Toro Rosso have now taken the plunge on the teenager, who admits that the news is a "dream come true".
"First of all, I would like to thank Dr Helmut Marko and Red Bull for all their trust and giving me the chance to make my Formula 1 debut in 2015 with Scuderia Toro Rosso," Verstappen said in a statement.
"Ever since I was seven years old, Formula 1 has been my career goal, so this opportunity is truly a dream come true."
Vergne is 13th in the drivers' rankings, having registered 11 points for Toro Rosso so far in the 2014 campaign.