After nearly four days existing milkshakes, the 61-year-old American toasted his achievement with champagne on Saturday. Asked what he would do next, he said: "Catch up on some sleep."
Ground control said Fossett broke the airplane distance record of 40,210km while his lightweight experimental plane was flying over Shannon, Ireland, late on Saturday.
Generator problems then forced him to land the Virgin Atlantic GlobalFlyer at Bournemouth in southern England instead of at a military air strip in nearby Kent.
"I was really lucky to make it here today, there was a lot going on," Fossett told reporters after he landed.
"The tension of the final part really took it out of me, but I will be fine in the morning."
Fosset completed his journey around the globe - and then some - over 3½ days despite losing about 750lbs of fuel during his take-off on Wednesday from the Kennedy Space Centre in Florida because of a leak.
The adventurer burst two tyres when he landed at Bournemouth airport on battery power. The generator had failed over Ireland just after he broke the record.
Other firsts by Steve Fossett:
17-21 February 1995: First solo balloon flight across the Pacific Ocean.
8-11 January 1996: First solo round-the-world balloon attempt.
19 June - 4 July 2002: First successful solo balloon flight around the world.
7 February- 5 April 2004: Breaks the round-the-world sailing record by six days (58 days, nine hours, 32 minutes and 45 seconds).
28 February- 3 March, 2005: First solo, non-stop flight around the world in an aeroplane.
8-11 February 2006: Longest non-stop flight by an aeroplane.
Richard Branson, his friend and sponsor who flew behind him in a chase aircraft for the final leg, said: "We told him he had to land alive.
"He actually had to land alive, because if he didn't land alive he wouldn't get the record."
The aircraft landed with 200lb pounds of fuel remaining from the 18,000lb loaded at take-off.
Its windscreen was so heavily iced that Fossett could barely see a few metres when he landed, his team said.
Fossett took off on Wednesday from Florida and flew solo eastward around the world before making a second crossing over the Atlantic to land in Britain.
He broke the record over Ireland, outlasting the ballooning distance record set in 1999 by Brian Jones and Bertrand Piccard as well as the 1986 distance record for an aircraft, set by Dick Rutan and Jeana Yeager on a nine-day flight in 1986.
Fossett piloted GlobalFlyer to an altitude of about 45,000 feet (13,720 metres) to take advantage of the high-speed jetstream flowing west to east over the northern hemisphere.
More information about the flight and aircraft can be found at http://www.virginatlanticglobalflyer.com/