Fossett and his co-pilot Mark Rebholz spent more than 18 hours in the air in a replica World War I bomber equipped with just a compass and a sextant for navigation, the Scotsman reported.
The two men landed their open-cockpit biplane Saturday on the eighth hole of the Connemara golf links in Clifden, Ireland -- recreating the 1,875 mile flight made 86 years ago by Arthur Whitten Brown and John Alcock.
The flight from Newfoundland, Canada, was the third in a series of flights re-enacting the epic journeys made by the Vickers Vimy aircraft during the early 20th century, the newspaper said.
Fossett spokeswoman Rosemary Dawson said the pair were speechless after their journey.
"They could barely walk, their legs were like jelly," she said.
Alcock and Brown's transatlantic journey in 1919 took place eight years before Charles Lindbergh's more famous solo flight.
2014: The Year in Music [PHOTOS]