The Virgin Atlantic GlobalFlyer aircraft, with a wingspan as wide as an 11-floor building is tall, lifted off from a runway at the Kennedy Space Centre normally used for space shuttle landings at about 1230 GMT on Wednesday.
Fossett had initially planned to start the record-breaking attempt on Tuesday, but had to delay by a day due to a fuel leak.
He is hoping to break by 1126 km (700miles) the 42,431km (26,366-mile) non-stop distance record set in 1986 by Dick Rutan and Jeana Yeager in a nine-day flight.
The aviator adventurer plans to cover 41,978km (26,084 miles) in three and a half days.
During his 80 hours in the air, Fossett will take power naps no longer than five minutes each and drink a steady diet of nutritious milkshakes.
Fossett expects the flight to last
The flightplan will take him over the Atlantic, across Africa, Saudi Arabia, India, China, Japan, the Pacific Ocean, Mexico, and the United States and then back over the Atlantic before landing at Kent International Airport outside London.
Fossett needs to get his glider-like plane up to an altitude of about 45,000 feet (13,720 metres) to take advantage of the naturally occurring high-speed jet stream flowing from the west to the east over the Northern Hemisphere.
In addition, the air temperature at takeoff had to be 12.22 C (54 F) or cooler for GlobalFlyer’s single engine to build enough thrust to ease the craft off the runway.
The plane weighs more than 11 tonnes when fully fueled.
Last March, Fossett flew around the globe alone for 67 hours, two minutes and 38 seconds without stopping and refueling in a trip that covered 36,989km.