The 26-year-old, who has been capped 16 times by his country, has agreed a two-and-a-half-year deal with the struggling Premier League club.
Narsingh will wear the number 28 shirt and 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."
Narsingh leaves PSV having won back-to-back Eredivisie titles, scoring 14 goals in 62 league games across those two campaigns.
Phillip Cocu's side have fallen to third - eight points behind leaders Feyenoord - this term, however, with Narsingh netting three times in 23 matches in all competitions.
The former Heerenveen player, who spent time in Ajax's youth system, was set to be out of contract in the summer.