A fee was agreed with the Welsh club on Saturday for the 27-year-old, who has signed a three-year deal and could debut against Manchester City on Monday night.
"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.
"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."
Vorm is set to be Swansea’s number one after previous incumbent Dorus de Vries moved to Wolves earlier in the summer.