The 61-year-old US aviator lifted off from Cape Canaveral, Florida, at 7.22am on a 41,978km trip that he hopes to complete in 80 hours.
But there were nervous moments as the aircraft needed 3,352 metres of runway to get off the ground, 457 metres more than expected.
"I couldn't have aborted if I had wanted to and I hit two birds ontake-off. The climb was very physical and it was so hot in the cockpit that the instruments stopped working," Fossett said.
Richard Branson, the billionaire Virgin Atlantic airline boss who is backing Fossett's bid, estimated the mercury nudged 54.4C on board, but he was still optimistic, putting his friend's record-breaking chances at "50/50".
Chief engineer John Karkow was less optimistic about the jet stream tail winds which, while strong from Africa through to the Middle East and over China, weaken over Hawaii and the Pacific.
At 2300 GMT, he was close to the island of Tenerife, flying at just over 592.6 kilometres per hour (320 knots) and at an altitude of nearly 11,900 meters, according to his web site.
His speed is a little quicker than the expected 470kph predicted by his support team.
Fuel critical
Staff at mission control in Crawley, southeast England, will monitor
Fossett's progress, in particular whether he has enough fuel to go the distance.
The flight is the second time he has made an attempt at the record.
Last March, he landed in Kansas after flying around the globe solo for 67 hours, two minutes and 38 seconds without stopping or refuelling in a trip spanning 36,989km.
His newest adventure would take him 1,126km further than the 1999 around-the-world balloon trip by Brian Jones, a Briton, and his Swiss partner Bertrand Piccard on the Breitling Orbiter III.
If everything goes according to plan, Fossett will also beat the distance record set by Dick Rutan and Jeana Yeager in their nine-day, non-stop trip around the world without refuelling aboard the Voyager aircraft in 1986.
That trip logged a total of 40,212km.
Fossett plans to fly eastward on a route that will vary according to the wind, probably passing over central Africa, Saudi Arabia, India, China and southeastern Japan before traversing the Pacific and reaching Mexico.
He then plans to fly past Cape Canaveral and go over the Atlantic a second time before landing at Kent International Airport in Britain, near London.
The flyer's first attempt at take-off was postponed on Tuesday due to strong winds and a fuel leak.
Record hunter
Thrill-seeking Fossett, who has set records in sailboats, gliders and hot air balloons, has said that this latest feat "will take me to the very edge of my ability and endurance".
The Virgin Atlantic GlobalFlyer was designed by aviation pioneer Burt
Rutan, creator of SpaceShipOne, the first private manned rocketship to go into space in 2004.
Rutan also designed the Voyager flown by his brother Dick in 1986.
The special aircraft is 13.4m long and has a wing span of 34.7m.
It weighs a total of 9.98 tonnes, including eight tonnes of fuel.
Fossett will take several five-minute naps during the flight.
The cockpit is equipped with an alert system to rouse the pilot if he falls asleep.