The 17-year-old goalkeeper joins Michael Laudrup's side having represented the Slovenia Under-17s on five occasions, and has recently been called up to Under-19 squad, while helping Domzale to a third-placed finish in Prva Liga last term.
Zabret is confident he can adapt to the fast-paced nature of the Premier League, insisting he did not take the decision to leave his homeland lightly.
"It is true. I am coming to Swansea City," the teenager told Sportal.
"I got some offers this summer, even West Brom and Sporting Lisbon wanted me. But I chose Swansea City some time ago.
"That was a decision that was taken after talking with my family. I believe that my decision is the right one.
"I know I will have to work hard to prove myself but I am ready for that and I believe that I will succeed in Premier League."