The 27-year-old, capped five times by Holland, has signed a three-year contract with the Premier League newcomers.
He could make his Swansea debut against Manchester City on Monday.
Vorm is relishing his role in manager Brendan Rodgers' team as the new season approaches, and revealed Premier League stars past and present backed his move.
He told Swansea's official website: "I've spoken with guys like Nigel de Jong, Robin van Persie, Rafael van der Vaart and Ruud van Nistelrooy and they all same the same - the Premier League is a beautiful place.
"The Premier League is the biggest league in the world and to be part of it is a massive opportunity.
"It is a huge challenge for the club because we are new to the league, but it is a fresh challenge too."
Vorm is set to be Swansea's first-choice goalkeeper for the new season, following the departure of Dorus de Vries to Wolves.
"I know Dorus was very popular here, and he did very well," said Vorm.
"Dorus got a move to Wolves, so that leaves an opportunity.
"Hopefully I will take that opportunity. I know I will fit into the style at Swansea - it's not like the other British clubs where the goalkeeper is told to hit it down the pitch.
"So if I can impress here then hopefully I can help my chances with the Dutch national team.
"But, firstly, I have to play well for Swansea and help the team in the Premier League."