He spent the entirety career with Hajduk Split. Although a talented goalkeeper, for a great part of his career he had to be a substitute to Vladimir Beara, who was named by legendary Soviet goalkeeper Lev Yashin as the greatest keeper of all time. He still managed to become the second-most-capped Hajduk Split goalkeeper ever, scoring 29 goals! He was also known as an excellent penalty taker. Beara claimed that he has never seen a better penalty taker than Ante Vulic.

He has won two national championships (1952 & 1955) with Hajduk.
His son Zoran Vulic was was a long-time and well known stopper of Hajduk.