The US-owned team, in their 11th season and with Toyota Gazoo Racing as title sponsor, posted digital renders of the VF-26 car to be raced by French driver Esteban Ocon and Britain's Ollie Bearman.
"It feels almost a bit surreal to be unveiling a new car this early in the year," said team principal Ayao Komatsu in a team Q&A.
"It’s been a monumental effort from everyone on the team to work with such a tight turnaround time from the end of last season to putting cars on track in January."
The sport is embarking on possibly its biggest ever technical overhaul with a new engine and aerodynamic era. Testing starts behind closed doors in Barcelona on January 26.
Last season finished in Abu Dhabi on December 7, with Ferrari-powered Haas finishing eighth overall.
"I think we can forget everything that we've learned since go-karts on how to go fast but it will be interesting to learn a new driving style and hopefully find speed with it," said Ocon.
"All of our senses, how we feel - we’ll need to think a lot more while driving about what to do, to go quicker."
New engines could bring huge variation
The new generation of cars will be thinner and lighter with narrower tyres and a 50/50 split on internal combustion, using sustainable fuel, and electric power.
Drivers will be able to use boost mode for maximum power from the engine and battery, anywhere on the track, at the push of a button while overtake mode replaces the old Drag Reduction System (DRS).
Cars also have movable front and rear wing elements.
Komatsu expected a "huge variation" between teams initially because of the new power units and aerodynamic changes.
Mercedes are supplying four teams and Ferrari three, including newcomers Cadillac, with Red Bull's two using their own unit and Audi and Honda (Aston Martin) providing engines to one each.
"On the aerodynamic side, it’s completely open and development will happen fast," said Komatsu. "A pecking order may get established in the first four races pretty quickly, but I think it’s going to be a very dynamic season.
"What you see in race one and race two, I expect will be totally different when we come to the final races of the year."
Ocon said the Haas had good balance and grip in the simulator and expected the biggest challenge to be on the engine management and hybrid side.
Bearman, a rookie last season, said stepping into the unknown was good and bad.
"On one side I feel like we can really have an impact straight away, but also it's horrible not knowing," said the 20-year-old.
"We don't know how we stack up, and we won’t know until qualifying in Australia. Even then, I feel like in the first few races reliability is going to be playing a big factor.
"There are going to be teams and people making mistakes with these new regulations. It's going to be tough to establish a true pecking order.