The 24-year-old centre-back has signed a four-year contract, committing himself to Craven Cottage until June 2022.
Mawson was an ever-present for Swansea in the Premier League last season, impressing despite their eventual relegation and earning a call-up to Gareth Southgate's England squad in March.
He did not feature in either of the friendlies against Netherlands and Italy and missed out on the final 23-man squad for the World Cup in Russia, but the former Barnsley defender can now press his international ambitions once more in the top flight.
"I'm really happy to get this over the line and join Fulham," Mawson told his new team's official website.
"I'm excited by the project going on here and the football being played last season was lovely on the eye but also effective. I can't wait to be a part of it and get going.
"I'm excited to be a part of this great club moving forward and to help achieve success in the Premier League."
Mawson is the latest arrival of an eye-catching transfer window at Fulham following their promotion via the Championship play-offs last season.
Aleksandar Mitrovic returned on a permanent deal from Newcastle United earlier this week, while Nice's highly rated midfielder Jean Michael Seri and German World Cup winner Andre Schurrle – the latter on loan from Borussia Dortmund – were their other high-profile recruits.
Slavisa Jokanovic's side host Crystal Palace in their Premier League opener next Saturday.