Narsingh, who has signed a two-and-half-year deal at the Liberty Stadium, said he believed the Swans could get clear of relegation danger.
Arsenal have sent teenage midfielder Dan Crowley on loan to Dutch club Go Ahead Eagles for the rest of the season after recalling him from Oxford.
Martin Odegaard has pledged to "prove what he can do" after joining Dutch side Heerenveen on loan from Real Madrid until June 2018.
Real Madrid's Martin Odegaard is set to seal a loan to Heerenveen, with the Dutch club saying the 18-year-old will be presented on Tuesday morning.
Liverpool have confirmed that young midfielder Pedro Chirivella has joined Dutch side Go Ahead Eagles on a loan until the end of the season.
Marco van Ginkel has signed a new contract at Chelsea until June 2019 and will rejoin PSV Eindhoven on loan in January.