The aircraft - called Solar Impulse-2 - took off from the Emirate, heading east to Muscat in Oman. Over the next five months, it will skip from continent to continent, crossing both the Pacific and Atlantic oceans in the process.
Andre Borschberg was at the controls of the single-seater vehicle as it took off. He will share the pilot duties in due course with fellow Swiss, Bertrand Piccard.
The plan is stop off at various locations around the globe, to rest and to carry out maintenance, and also to spread a campaigning message about clean technologies.
Before taking off, 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."
Solar impulse will cover 2:35000 km around the world
The project has already set a number of world records for solar-powered flight, including making a high-profile transit of the US in 2013.
But the round-the-world venture is altogether more dramatic and daunting, and has required the construction of an even bigger plane than the prototype, Solar Impulse-1.
This new model has a wingspan of 72m, which is wider than a 747 jumbo jet. And yet, it weighs only 2.3 tonnes.Its light weight will be critical to its success. So, too, will the performance of the 17,000 solar cells that line the top of the wings, and the energy-dense lithium-ion batteries it will use to sustain night-time flying.
Operating through darkness will be particularly important when the men have to cross the Pacific and the Atlantic. The slow speed of their prop-driven plane means these legs will take several days and nights of non-stop flying to complete. Piccard and Borschberg - whoever is at the controls - will have to stay alert for nearly all of the time they are airborne.
They will be permitted only catnaps of up to 20 mins - in the same way a single-handed, round-the-world yachtsman would catch small periods of sleep. They will also have to endure the physical discomfort of being confined in a cockpit that measures just 3.8 cubic metres in volume - not a lot bigger than a public telephone box