He was born on the December 23, 1923 in Zagreb, Croatia. When he was just 13 and a half years old, he started playing first team Football for Viktorija, a lower league club,,using his brothers registration papers. When he was 20, he became the center-forward of Građanski Zagreb (today's Dinamo Zagreb). He was the top scorer of the Yugoslav First Division twice, in 1945 (8 goals) and 1954 (21 goals).He came to Partizan Belgrad in 1945 and played for them till 1958.
In those 13 years he played 468 games and scored 403 goals holding the club record for goals scored.
Bobek won two Yugoslav League Titles and four Yugoslav Cup's. He played in two World Cups, in Brazil 1950 (he scored one goal in the 4-1 win over Mexico) and in Switzerland 1954, he also played in two Olympic Games, in London 1948 (4 goals, Yugoslavia won the Silver Medal) and in Helsinki 1952 (also silver medal). On June 8, 1947 he scored a record 9 goals in a game against 14. Oktobar in Niš. He scored in total 38 goals in 63 matches for the Yugoslavia national team.
Bobek left a legacy as a coach in Greece. He was the first to implement the 4-3-3 system and, in 1964, he led Panathinaikos to the championship finishing the season without a single defeat. He also led the Athens club to the championship in 1965. Very controversially, in the 1970 season, he made the move to Panathinaikos' rivals Olympiakos.
He remained in the Serbian capital Belgrade after the breakup of Yugoslavia in the 1990s.
In 1995 he was named the greatest and most popular Partizan Belgrade player of all time.