Vettel announced his decision to leave the British-based constructor in October after winning four world championships, and was confirmed at Ferrari a month later.
Red Bull acted quickly to fill the gap left by the German with Daniil Kvyat coming in to partner Daniel Ricciardo for the new season, which begins in March.
Horner believes they have got a strong pairing for the new campaign and expects them to battle hard to return Red Bull to the top of the constructors' standings.
Speaking to the team's official website, he said: "We have an exciting new driver line-up next year in Daniel Ricciardo and Dany Kvyat.
"The two drivers get on very well and know each other.
"They both have a bit of banter outside the car, in the car they are both hungry, no-quarter-given racing drivers.
"That's going to be an exciting new dynamic and they are going to be pushing very hard."
But Horner knows the team must produce a car that will allow the young drivers to compete with speed of the Mercedes and Williams cars.
"Those guys [Mercedes] aren't going to stand still," he added. "It's down to the teams to try and catch Mercedes now and we have a lot of work going on with Renault to try and reduce that gap.
"Next year seems to have started already. The focus has never been more intense in trying to deliver a competitive car for next year."