The 36,800 km trip was also registered as the fastest nonstop flight around the world.
A cheering 5000-strong crowd and a high school marching band greeted Fosset as he stepped out of the tiny cockpit to be hugged by his wife Peggy and drenched in champagne by the project's financier, Sir Richard Branson of Virgin.
"I'm glad to be here and energised by the reception," he said. "I'm feeling better than I have for the past couple of days."
But "I might take a shower and I wouldn't mind finding a toilet. There are just certain things that are missing on this aircraft," said the man who lived on water and 12 chocolate-flavoured milkshakes during the flight.
Despite no sleep on the first night and only six one-to-three-minute naps thereafter, "I was in control and was able to make rational decisions. I don't think I made any major errors," he said.
Fossett, 60, said he thought the mission might be put off after the satellite navigation system of his experimental aircraft failed hours after leaving Salina. This was followed by the loss of 1,180kg of fuel, which was "siphoned out of the wings in the first hours of the flight".
But "there was a lot of preparation that went into this, so I would have been very disappointed not to get around the world."
He also expressed surprise over the time he spent in darkness. He expected the flight to last just under three days, but went through four nights as he was flying east chasing the sunrise.