The unmanned four-hour flight will test crucial systems, like the heat shield and parachute splashdown, on a spacecraft that could one day take humans to an asteroid, the Moon or Mars.
It is the first launch in more than 40 years of a US spacecraft intended to carry humans beyond the Moon.
Orion blasted off aboard a United Launch Alliance Delta IV Heavy rocket at just after 7am local time (12pm UK time) from Cape Canaveral in Florida.
Things you need to know about NASA’s Orion spacecraft
The 24-storey-tall rocket soared out over the Atlantic Ocean, punching through partly cloudy skies as it headed into orbit.
Cars packed roads for miles around the launch site as thousands tried to catch a glimpse of the event.
“I think it’s a big day for the world, for people who know and like space,” NASA Administrator Charles Bolden said in a NASA Television interview before the launch.
“Everything may not go right, but everything that does go right means that we’ve bought down one more risk on this vehicle.”
He called the launch “day one of the Mars era”.
Orion will orbit the world twice on its inaugural flight and will shoot for a high point of 3,600 miles, farther than any spacecraft built for humans has gone since the Apollo moon programme.
Sensors on the capsule should tell NASA if the temperatures inside were survivable for a potential crew, even as the spacecraft itself heated to 2,200 Celsius (4,000 degrees Fahrenheit) during re-entry to the Earth’s atmosphere at a velocity of 20,000mph.
About $370m (£235m) worth of equipment is at stake in the launch.
NASA has spent $9.1bn (£5.8bn) on Orion and the Space Launch System, which is meant to propel it with a crew on board.
The first test flight with people on board is scheduled for 2021, when total costs are projected to reach $19-22bn (£12-£14bn).
A journey to Mars could take place by the 2030s.