The 28-year-old turned down a new contract at former club Heerenveen, for whom he played for the last two years.
Mulder, who has signed a three-year deal, will contest the goalkeeper position with Lukasz Fabianski and Kristoffer Nordfeldt.
"I am very happy to be here. The opportunity has come and I have taken it with both hands," Mulder told the Swansea website.
Mulder, who will join officially in July, will become the fourth Dutch goalkeeper to join the Welsh club after Dorus de Vries, Michel Vorm and Nico Schroeder.
"There have been many Dutch players here, including some goalkeepers," Mulder added.
"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 Fabianski is here and Kristoffer Nordfeldt is here, so it is going to be difficult. But I am going to do my best."
Swansea have signed Dutch goalkeeper Erwin Mulder on a free transfer.