Heart head coach John van 't Schip said the pair will give good depth to the current list which possesses plenty of experience.
"Ante and Aziz have proved themselves to be excellent talents and trainers throughout their time at the Club, and I feel they will certainly add an extra dimension to our squad," he said.
"With youth a key focus of the Club's philosophy, we are pleased to have signed such promising youngsters. They are very raw talents that we are confident can develop into exceptional professionals while working with the likes of Simon Colosimo, Josip Skoko and John Aloisi.
"In relation to Aziz, we are very pleased to give him another opportunity at the elite level. One of the great benefits of more professional clubs in Australia is the greater opportunities it gives to young players to stay in the sport during their important development years."