Verstappen made the promotion from Toro Rosso in 2016 ahead of the Spanish Grand Prix, taking the place of the struggling Daniil Kvyat. Verstappen, who was 18 at the time, won his first race for the Bulls, making him the youngest race winner of all time, as well as the first-ever Dutch Grand Prix winner.
Still only 21 years of age, Verstappen has started the 2019 season strongly, finishing on the podium in Australia and finishing fourth in the two Grands Prix after.
"He's driven three very strong Grands Prix this year," Horner told Sky Sports F1.
"He was obviously unlucky not to be on the podium in Bahrain and had a go at Sebastian [Vettel] here after the second stop and drove a very mature race to bring it home fourth."
"He's done a remarkable job. During the course of last year, he really selected another gear and pretty much since Montreal onwards," Horner continued.
"He's very much at the top of his game and enjoying the position he's in."