The Red Bull and Honda marriage begins in Australia next year, after the Japanese manufacturer had provided power units to junior team Toro Rosso this season.
This came about after Red Bull had enough of Renault and the issues with their power units.
Verstappen was only outscored by Lewis Hamilton in the second half of the 2018 season, giving him confidence for next year.
“Hopefully it will be a long-term collaboration,” Verstappen said of the marriage.
“I don’t expect that everything runs smoothly at once, but you can’t expect that, I think. I will always be focussed, but you also have to believe in the project and be patient.
“I do not expect that we can really fight for the championship at the start of the season, but if we are just a little bit better than this year, we can be closer to the competition and run a consistent season, that is already an improvement for the championship.
“You do not necessarily need to have the best car.”