Goalkeeper Zabret, 17, joins on a two-year deal from NK Domzale while 19-year-old midfielder Gogic arrives on a free transfer from Olympiakos and has signed a one-year contract.
Both players spent time on trial at the Liberty Stadium last season.
Zabret said: "I'm very happy to be here. It is a great environment for me to develop and I'm looking forward to starting work.
"There are some great people at the club and I hope to get as much training with the first team as possible to help my development."
Gogic said: "I was very impressed with what I saw when I came here on trial and I'm delighted to have signed for Swansea.
"The aim is to win games for the U21s and test myself against some great players from other clubs."