No heavier than a car but with the wingspan of a Boeing 747, the four-engine, battery-powered aircraft relies on around 17,000 solar cells embedded in its wings.
The plane clocked an average speed of 80 kilometers an hour (50 miles per hour).
The pilots used oxygen tanks to breathe at high altitude and wore suits specially designed to cope with the extreme conditions.
They had to withstand temperatures inside the tiny cockpit ranging from minus 20 degrees to plus 35 degrees C (minus 4 degrees to plus 95 degrees F).
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Piccard has said he launched the project in 2003 to show that renewable energy "can achieve the impossible."
His dream has taken much longer than planned. The attempt was initially expected to last five months, including 25 days of actual flying.
But the aircraft was grounded in July last year when its solar-powered batteries suffered problems halfway through the trip.
The project was also beset by bad weather and illness, which forced Piccard to delay the final leg.
While in the air, the pilot was constantly in contact with mission control in Monaco, where a team of weathermen, mathematicians and engineers monitored the route and prepared flight strategies.
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A psychiatrist who made the first non-stop balloon flight around the world in 1999, Piccard had warned the last leg would be difficult because of the high temperatures.
"It's been two hours now I'm flying into high up and down drafts. And I can't even drink. It's really exhausting," he tweeted on Sunday.
But he did not show signs of fatigue when he landed.
"It was a project that was very difficult, a lot of people doubted we could do it, so of course for the team it's fantastic but also for all the people who believe in clean technologies," Piccard told reporters after landing.
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"The biggest challenge is to have an airplane that can fly perpetually, days and nights without refueling, because there is no fuel. And to overcome all the skepticism of the different key opinion leaders in this world who were saying: 'They cannot do it. It's impossible.'"
While the pilots do not expect commercial solar-powered planes any time soon, they hope the project will help spur wider progress in clean energy.
"We can hardly believe that we made it. It's still a little bit like in a dream. We have to realize that it's the reality," Piccard said.
"We have flown one after the other in the cockpit with Andre, 40,000 kilometers without fuel, and now the demonstration is done," he said. "It means that the rest of the world has to take it further."