It was reported last week that the Premier League club have agreed terms with the 17-year-old Slovenian.
"It is true. I am coming to Swansea City," Zabret told Sportal.
"I got some offers this summer, even West Brom and Sporting Lisbon wanted me. But I chose Swansea City some time ago."
The Swans get the new Premier League season underway at home to champions Manchester United on August 17.