The 29-year-old Polish international signed a four-year
deal, which will be activated upon the expiry of his Arsenal contract on
July 1, and becomes Garry Monk's first signing since taking over as
manager in February.
"I am very happy with the move, the decision and the club," he told the Swansea website. "For me, it was an easy decision to make.
"If I'm completely honest, the main reason I came to Swansea was because I want to be the number one goalkeeper. I want to play week-in, week-out. It's going to be a real fight, but I'm not afraid of that."
Fabianski, who has won 21 international caps, will compete with Dutch international Vorm for a starting spot at the Liberty Stadium after ending his seven-year spell at the Emirates.
The injury-prone Vorm, who underwent knee surgery in December, was named in the Netherlands' preliminary World Cup squad earlier this month.
Swansea also have German goalkeeper Gerhard Tremmel on their books.
Arsenal manager Arsene Wenger had said he had wanted to keep the goalkeeper, who was backup to first choice Wojciech Szczesny but started the FA Cup final earlier this month as the Londoners beat Hull City 3-2.