The 58-year-old ex-stockbroker crossed the finish line on his 13th day in the air when he passed 117 degrees east longitude off Australia's southern coast, the same line where he began his quest.
It was sixth time lucky for Mr Fossett, who had come close to death in his previous attempts to break the record.
He sounded calm when he called his mission control, saying simply: "It is a wonderful time for me."
He was scheduled to put the balloon down later in the day in Australia's desolate outback, according to his control centre at Washington University in Saint Louis, Missouri.
The BBC correspondent in Sydney, Phil Mercer, said the landing could yet prove challenging in the huge balloon but forecasted light winds should ease the descent towards Kalgoorlie or Adelaide.
Mr Fossett completed the circumnavigation during darkness, after covering nearly 20,000 miles (32,000 kilometres) around the southern hemisphere.
He faced fewer difficulties than on his previous aborted attempts and still has oxygen to spare.
But Mr Fossett has not yet cracked open a celebratory drink in his cramped capsule.
"I can't do very much celebrating here," he said.
"I do have a few bottles of Bud Light [which sponsored the trip] but I'm saving it for the landing.
"There's no one here to drink it with - that's the nature of solo flights."
During the flight in the silvery balloon, Mr Fossett often hurtled along at speeds up to 200 mph (322 km/h), at an altitude more familiar to jetliners.
The weather has mostly been kind, though the balloon was caught in a dangerous "yo-yo phenomenon" near the Andes when the craft went into a series of uncontrollable leaps and dives.
On Sunday, Mr Fossett broke his own four-year record for the longest
distance travelled by a solo balloonist.
In 1998 he travelled 14,235 miles (22,904 kilometres) from Argentina but the attempt ended with a dramatic 29,000 ft (8,700 metre) plunge into the Coral Sea.
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