"The adventure has started," Solar Impulse chairman Bertrand Piccard said emotionally, after pilot Andre Borschberg took off from Abu Dhabi's Al-Bateen airport at 7:12 am on the historic circumnavigation aimed at promoting green energy.
The 400 kilometre maiden leg to the Omani capital Muscat was expected to take around 12 hours.
After four hours' flying, Borschberg was on schedule, having already entered Omani air space and covered just over a third of the distance.
The takeoff by Solar Impulse 2, which was originally scheduled for Saturday but delayed due to high winds, capped 13 years of research and testing by Swiss pilots Borschberg and Piccard.
Live video streaming on the website monitoring his progress www.solarimpulse.com showed the pilot, wearing an orange jumpsuit, breathing into an oxygen mask.
"From Mission Control Center in #Monaco the engineers are helping me to perform Oxygen Mask tests from #SolarImpulse," he tweeted.
Borschberg had earlier attempted to give media interviews before calling his wife, according to the live feed.
Shortly before takeoff, the 63-year-old pilot tweeted that the "challenge to come is real for me & the airplane".
The wingspan of the one-seater plane, known as the Si2, is slightly bigger than that of a jumbo jet, but its weight is around that of a family car.
From Muscat, it will make 12 stops on an epic journey spread over five months, with a total flight time of around 25 days.
It will cross the Arabian Sea to India before heading on to Myanmar, China, Hawaii and New York.
Landings are also earmarked for the midwestern United States and either southern Europe or North Africa, depending on weather conditions.
The longest single leg will see a lone pilot fly non-stop for five days and nights across the Pacific Ocean between Nanjing, China and Hawaii, a distance of 8,500 kilometres.
The federal department of foreign affairs issued a statement wishing the Solar Impulse flight "bon voyage".
The Swiss government regards the plane as an "ambassador for sustainability" and a way to showcase Switzerland's innovativeness as a nation in terms of sustainable development and environmental protection.
"I applaud this pioneering venture, which will show our younger generations that a world we thought impossible to attain is now within our grasp," Foreign Affairs Minister Didier Burkhalter said in a statement.
"Progress and respect for our planet — that is the message Switzerland is giving with Solar Impulse," Burkhalter said.
Ambassador Nicolas Bideau, head of Presence Switzerland, was in Abu Dhabi to see Solar Impulse take off.
And Swiss embassies, consulates and other offices have planned a number of events in the next few weeks in conjunction with the flight, in particular in those countries where the aircraft will land.