There was a mixed reaction from fans on social media at the livery unveiling, with some fans begging the team not to alter the design, others left revolted by the dramatic departure while one supporter compared it with the red and black face of Star Wars villain Darth Maul.
Red Bull have described the new appearance as a "one-off livery".
They will use Honda power units for the first time, and the vehicle carries Honda branding on its nose and engine cover.
"I'm very excited to just get started with the engine", Verstappen said.
Both drivers are at Silverstone today for the first run of the new vehicle.
Verstappen completed 39 laps with the team reporting that the auto ran "faultlessly".
"Up until Australia you can't really set goals - it's a bit blind".
Verstappen will get the first proper taste of his new Red Bull during next week's first pre-season test at Barcelona's Circuit de Catlunya.
Haven't we seen this before from Red Bull?
West Indies vs England: Shannon Gabriel warned over clash with Joe Root
Root enjoyed a fine day at the crease, scoring a 16th Test century and finishing 111 not out as England built a lead of 448 runs. You have responsibility to go about things in a certain manner on the field and it felt appropriate to act how I did'.
Renault and Red Bull broke ties last season largely because of the reliability issues that Red Bull were facing.
The former world champions launched their 2018 vehicle in dark black and blue colours before reverting to their traditional look for the start of testing.
For the new RB15, the team appeared to have ditched the famous Red Bull logo that has featured on every one of their cars since they took over Jaguar ahead of the 2005 campaign.
What can we expect from Red Bull in 2019?
After five years without championship success, Red Bull is switching from Renault power to Honda this year.
"Formula 1 is the pinnacle of motorsport".
The 2019 F1 season brings the dawn of a new marriage as Red Bull pair up with works engine supplier Honda in a bid to return to championship-winning ways.
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.