André Borschberg and Bertrand Piccard took off the aircraft, named Solar Impulse-2, from Abu Dhabi, heading to Muscat, Oman.
After Oman, the plane will head to the US, India, Oman, Myanmar, China and several other regions.
The 400km first-leg flight is part of a 35,000km journey, which is anticipated to take about five months.
It is claimed to be the first airplane able to fly day and night without a drop of fuel.
Borschberg told BBC News: "I am confident we have a very special aeroplane, and it will have to be to get us across the big oceans.
"We may have to fly for five days and five nights to do that, and it will be a challenge.
"But we have the next two months, as we fly the legs to China, to train and prepare ourselves."
The project team said in a statement, which was published on its website, "By writing the next pages in aviation history with solar energy, and voyaging around the world without fuel or pollution, Solar Impulse’s ambition is for the world of exploration and innovation to contribute to the cause of renewable energies, to demonstrate the importance of clean technologies for sustainable development; and to place dreams and emotions back at the heart of scientific adventure."
Image: In February 2015, Solar Impulse 2 soared across the skies of Abu Dhabi during its first test flights in the emirate. Photo: Courtesy of Masdar.
