The 28-year-old arrives at the Liberty Stadium having turned down a new contract at Eredivisie club Heerenveen, for whom he played for the last two years.
Mulder has signed a three-year deal and becomes Swansea manager Paul Clement's first signing of the summer.
He began his career at Feyenoord, where he made 120 appearances, had a season on loan at Excelsior in 2008-09, and joined Heerenveen in 2015.
In all, he has played more than 250 senior games in his native Holland.
Mulder will compete for the number one spot at the Liberty Stadium alongside Lukasz Fabianski and Kristoffer Nordfeldt, who he succeeded at Heerenveen when the Sweden international joined Swansea.
"I am very happy to be here," Mulder told the official Swansea website.
"Now the opportunity has come and I have taken it with both hands.
"The Premier League is the biggest league in the world. As a player, you want to be part of that."
Mulder becomes the third Dutch goalkeeper to join Swansea with Dorus de Vries and Michel Vorm having played notable roles there in the past decade.
"There have been many Dutch players here, including some goalkeepers," Mulder said.
"A lot of them have done well here so it is nice for me to be here now.
"I know a little bit about the club. I spoke with Leroy Fer and Mike van der Hoorn.
"They told me some good things about the club.
"Of course I want to challenge to play here, but Lukasz is here and Kristoffer is here, so it is going to be difficult. But I am going to do my best."
