ABU DHABI, United Arab Emirates—With its wings stretched wide to catch the sun’s energy, a Swiss-made solar-powered aircraft took off from Abu Dhabi just after daybreak on Monday, in a historic first attempt to fly around the world without a drop of fossil fuel.

Solar Impulse founder André Borschberg was at the controls of the single-seat aircraft when it lumbered into the air at the Al Bateen Executive Airport. Mr. Borschberg will trade off piloting with Solar Impulse co-founder Bertrand Piccard during layovers on a 22,000-mile...