Anfield chief executive believes 'smart and sustainable' transfer policy is paying off for Merseyside outfit.
Watford captain Troy Deeney has signed a new five-year contract with the club ending speculation about his future.
Sky Sports sources on Friday revealed last season's Capital One Cup winners had agreed terms with NK Domzale for the 17-year-old.
And Zabret has now revealed he chose a move to Swansea over their Premier League rivals West Bromwich Albion, as well as Portuguese giants Sporting Lisbon.
"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."
Zabret will inevitably be one for the future for Swansea given they already have reliable goalkeepers in Michel Vorm and Gerhard Tremmel.