Alexandris began his career where he was born and raised, in Pelopas Kiato and in 1986 played for Veria.
At the dawn of his career he was also both player and manager for APOP Kinyras during the team's first participation in the Cypriot First Division.
Alexandris made 42 appearances and scored 10 goals for Greece,[3] making his debut on 27 March 1991.
He was a member of the squad that participated in the 1994 FIFA World Cup group stage in the United States.
He left Kerkyra after a disagreement with the club's owner and then moved to Olympiacos as the manager of the under-21 squad.