The plane will head over the Arabian Sea to India, Myanmar and China, then cross the Pacific Ocean, the United States, the Atlantic, southern Europe and finally North Africa before returning to its point of departure.
Speed at night will be limited to 46 kilometers (28.75 miles) per hour to prevent the batteries from being run down too quickly. The pilot sits on a "business class" seat where he can take short naps, although lavatory conditions are described as basic.
He will be helped by a virtual co-pilot that will wake him up and report back any problems to mission control in Switzerland.
The masterminds of the project are Bertrand Piccard, the scion of a dynasty of Swiss scientists-cum-adventurers, and Andre Borschberg, a former Swiss air force pilot. Piccard made history in 1999 by becoming the first person to fly around the world in a hot-air balloon.
He and Borschberg founded Solar Impulse a dozen years ago, frustrated with traditional airplane makers who refused to take them seriously. The pair argued that more efficient solar cells and batteries, coupled with ultra-light materials, could make a sun-powered plane a reality, even at night.
"This is really an experimental project of exploration, so everything is new," Piccard said on Monday.
"We have to jump into the unknown at every moment, and today was one of these moments, where the first plane that should fly around the world next year had to be tested, fully tested, and I think for Andre and myself it was an incredible emotion."
Borschberg said the test flight was "a very important step."
"Our goal is to fly around the world next year, and we needed an airplane able to travel the first step, a flying laboratory. This airplane will travel many days and many nights over the ocean, so it's a big step up from the first one."