Swansea said on their website that Mulder had signed a three-year deal and will compete with Polish international Lukasz Fabianski and Swedish keeper Kristoffer Nordfeldt for the position.
"Now the opportunity has come and I have taken it with both hands," he said. "The Premier League is the biggest league in the world. As a player, you want to be part of that.
"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."
Mulder will join his new team mates for pre-season training on Monday.
Swansea finished 15th last season after a successful battle against relegation.
(Reporting by Alan Baldwin; Editing by Alison Williams)
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