Fer, who played and scored for the Dutch at the 2014 World Cup, is Swansea's second signing of the transfer window, joining former Chievo striker Alberto Paloschi.
The 26-year-old, capped 11 times by Netherlands, will be hoping to avoid a third straight relegation from the Premier League.
Fer was part of the Norwich City side that dropped out of the top flight in 2014 and a year later suffered the same fate with QPR.
His career began at Feyenoord and he featured in 100 matches for the club, making his debut as a 17-year-old.
Fer also had a spell with Twente Enschede before moving to England.
Swansea, who recently installed Francesco Guidolin as manager following the sacking of Garry Monk, are 15th in the table and visit West Bromwich Albion in the league on Tuesday.
(Reporting by Martyn Herman; Editing by Tony Jimenez)
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