Mawson scored two goals in 38 league starts for Swansea last season as the Welsh club were relegated from the top flight.
"I'm really happy to get this over the line and join Fulham," Mawson told the club's website.
British media reports said Fulham paid Swansea 20 million pounds for the highly-rated centre back.
"I'm excited by the project going on here and the football played last season was lovely on the eye but also effective and I can't wait to be a part of it and get going," he added.
Mawson's performances for Swansea last term caught the eye of England manager Gareth Southgate, who called him up for friendlies in March against the Netherlands and Italy.
However the 24-year-old defender did not make his debut and was then ruled out of contention for a place in the World Cup squad after having knee surgery in May.
Fulham have recruited several players after their return to the Premier League for the first time since the 2013-14 season, including striker Aleksandar Mitrovic, goalkeeper Fabricio Agosto Ramirez 'Fabri' and playmaker Andre Schuerrle.
Fulham host Crystal Palace in their opening league match on Aug. 11.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Ken Ferris)
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