After finishing second and fifth respectively in last year's title race, as Red Bull's Sebastian Vettel dominated in clinching back-to-back world titles, the Woking-based marque are determined for this to be their year.
The MP4-27, which bore a typical silver livery that has been the case for a few years now, will hit the track for the first time in Jerez on Tuesday, with Button at the wheel.
Button said: "It's a very exciting day for us all. It's the moment when we see how hard we've all been working.
"I want to say thanks to the guys who have been working flat out throughout the winter to develop this car.
"Testing is now very important. We've got to come out of the box and be strong.
"Testing is what it says on the tin, it's about finding your feet, about gaining in confidence in the team you're working with and the car you're driving."
After admiring the car for the first time, Hamilton said: "I think it looks fantastic. It's great to be here after a great winter.
"The car is the most refined looking we've had for some time, so I'm excited to get back into it."
Ahead of his sixth season with the team, Hamilton added: "It feels very much like only yesterday when I went up to (former team boss) Ron (Dennis) and said I wanted to race for his team.
"But we've been competing at the front all those years. We've strength in depth, a great foundation from which we work. This is a team that never gives up."
Caterham were the first to launch last week, with their car sporting a 'duck-billed platypus' shaped nose, the result of the meeting between front suspension and chassis.
That has been based on new regulations that decree a higher nose, with many suspecting that would be the way forward, leading to it being described as 'ugly'.
However, the new McLaren remained very much true to past cars, with a smooth transition across the chassis from cockpit to front wing.
Button said: "This is a beautiful car, which for me is important. Many you see will not be."
Hamilton concurred, adding: "We're coming in massively motivated, very fresh, and when you have a good-looking car, generally it's a good car, so hopefully that is the case."
Hamilton and Button represent a third of the six world champions that will be on the grid this season for the first time in the sport's history.
The duo are joined by Vettel, Michael Schumacher, Fernando Alonso and the returning Kimi Raikkonen, who this season will be driving for Lotus.
Hamilton added: "We love to have competition. It's great to have so many great drivers. Hopefully there won't be too many more added to it.
"It's great for fans, great for the sport."
Button and Hamilton took different routes over the winter, with the former preferring warm climes, whilst Hamilton opted for time in a chillier Colorado.
Button said: "It was great. I spent time with family and friends, and it was good to be away from the car for a while.
"But after a few weeks I couldn't wait to get behind the wheel again.
"I came back on January 5. I spent some time in the simulator, and I've just been getting back to the way of life of a driver and spending time at the MTC (McLaren Technology Centre)."
As for Hamilton, he said: "For me it was nice to be away from it all, to get the energy back, to refresh, to start anew
"I altered training, I balanced things a bit better, spent more time with family and friends and I had a great break.
"Thanks to (team principal) Martin (Whitmarsh) for giving me such a good break."
Whitmarsh was certainly proud of the latest McLaren revealed at the MTC as he said: "It looks beautiful at the moment, but they only really do look beautiful when they win races.
"Beauty, though, is more than skin deep. It's about what's underneath.
"Of course, it's no surprise to anyone here that our goal is to win two championships. That's what we try to do every year.
"We don't like losing or coming second and the last two years have had their frustrations. But we've two drivers who are fierce competitors, they want to beat each other very badly, yet they spur each other on."
McLaren's winter testing form last year was awful as they took a wrong direction with the car, but Whitmarsh is quietly confident such mistakes will not be repeated.
"We won't know until qualifying in Australia where this car is," he added. "Last year we had, by McLaren standards, an abysmal winter testing session where we didn't have pace.
"It was a relatively stressful process, and of course I'd be much happier to be not fighting those issues.
"There's a lot of work gone into this car and we believe we're in a better position this winter compared to last."