After starting his career with Brommapojkarna in Sweden, he joined Dutch club Heerenveen in 2012.
Swansea have released goalkeepers Gerhard Tremmel and David Cornell so Nordfeldt, who has five international caps, will rival Poland's Lukasz Fabianski as first choice.
He is the Welsh club's third newcomer of the close season.
Swansea, who finished eighth last term, had already signed Ghanaian striker Andre Ayew and French full back Franck Tabanou.
(Reporting by Steve Tongue, editing by Tony Jimenez)
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