Solar Impulse founder Andre Borschberg was at the controls of the single-seater when it took off from the Al Bateen Executive Airport.
Mr Borschberg will swap piloting duties with Solar Impulse co-founder Bertrand Piccard during stop-overs.
The Swiss pilots say their aim is to create awareness about replacing “old polluting technologies with clean and efficient technologies.”
The plane is expected to reach its first destination - Muscat, Oman - after about 10 hours of flight.
Some legs of the trip, such as over the Pacific and Atlantic oceans, will mean five or six straight days of flying solo.
The lightweight Solar Impulse 2, a larger version of a single-seat prototype that first flew five years ago, is made of carbon fibre and has 17,248 solar cells built into the wing that supply the plane with renewable energy. The solar cells recharge four lithium polymer batteries.
The company says the plane has a 236ft wingspan, larger than that of a Boeing 747, but only weighs about as much as a car at around 5,070 lbs.
The plane in June made an inaugural flight of two hours and 17 minutes above western Switzerland, just two months after it was unveiled last year.
After Oman, the plane will head to India, where it will make two stops, then to China and Burma before heading across the Pacific and stopping in Hawaii.
Then it will head to Phoenix, Arizona, and New York’s biggest airport, John F Kennedy International. The path across the Atlantic will depend on the weather and could include a stop in southern Europe or Morocco before ending in Abu Dhabi.
The two pilots are expected to return to Abu Dhabi in late July or even August.
Mr Borschberg and Mr Piccard say they want to push politicians, celebrities and private citizens to “confront the Conference on Climate Change of the United Nations, which will define the new Kyoto protocol in December 2015 in Paris”.
Solar Impulse supporter Prince Albert of Monaco was present at the Monaco control centrr during take-off.
The UAE-based Masdar, the Abu Dhabi government’s clean-energy company, is a key sponsor of the flight.
Additional sponsors include Omega, Google and Moet Hennessey, among others.
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