The 26-year-old has agreed a two-and-a-half-year deal with the struggling Premier League club.
Narsingh, who will wear the number 28 shirt, is the first signing made by Paul Clement since he took over as head coach on January 3.
Speaking to the club's official website, Narsingh said: "I've looked at the Premier League for two or three years now, and Swansea always play good football.
"That's why, when Swansea came in for me, I knew I wanted to play here.
"This is the best league, and with Swansea playing good football I knew it was a good club for me.
"I'm 26 now and it's a good age to come to the Premier League. I won two titles in Holland, so it is a great time to come here."