Vourtzoumis won three European titles with three different Greek basketball teams. In 1993 he played for Aris BC and won the Cup Winners' Cup against Efes Pilsen S.K. at Torino. In 1996 he played for Panathinaikos BC and was the winner of the European Champion's league (Euroleague) at Paris. In 2001 Vagelis Vourtzoumis won the Saporta Cup with Marousi BC.
He won three Greek Championships (1989,1990,1991) and two Greek Cups (1990,1992) while playing for Aris BC. He has also won one Greek Championship (1998) and one Greek Cup with Panathinaikos BC (1996). He also had eight caps with the Greek national basketball team (5.8 points per game).