They will use Honda power units for the first time, and the auto carries Honda branding on its nose and engine cover.
Verstappen, the former teammate of Australian Daniel Ricciardo, is set to be among Hamilton's chief challengers this year, and the young Dutchman put his new vehicle through its paces on Wednesday.
Red Bull will begin the campaign, which starts in Australia on March 14-17, without Renault power for the first time in 13 years as Honda step up into the limelight after a development season with Toro Rosso.
However, Red Bull have previous in teasing fans with maverick designs that were only used in pre-season testing, only to revert to a more conventional look in time for the opening race of the season.
"I want to get the best out of myself, but you have to see what the auto and engine are going to do".
Both drivers are at Silverstone today for the first run of the new vehicle.
"It's a really nice group of people to work with as well".
The team is hopeful a switch to Honda will yield more consistent results. However, the shift from Renault to Honda is supposed to sort out all Red Bull issues and put them in contention for a title.
Daniel Ricciardo's departure to Renault has opened the door for 23-year-old Pierre Gasly to stake his claim as a race victor of the future.
"I just can't wait to get started now for Barcelona and start working towards Melbourne", Verstappen added.
"We are expecting a lot", said Verstappen. "It was a very positive day so very happy about it". "At the moment, I am of course very optimistic, but also realistic and I think time will tell how we are going to perform".
The RB15 vehicle was launched with temporary red-and-black livery. Now we can go testing properly, we'll see what we can get out of that and we'll be able to understand the auto and the engine a bit better.
"Of course today is all about filming, but it's also a really valuable opportunity to check that all the systems work and that the auto is fundamentally in good shape before we head to Barcelona next week where hopefully it will be a bit warmer!" said team boss Christian Horner.
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