Alexandris began his basketball career in December 1965 at Anagennisi Thessaloniki, where his athleticism and talent quickly stood out, attracting the interest of many major teams.

The promising youngster was approached by two great personalities of Thessaloniki basketball, Orestis Angelidis of PAOK and Anestis Petalidis of Aris, who recognized his sporting value and perspective.

The transfer took place in 1970 and due to a prohibitive regulation of the time, Alexandris, along with Charis Papageorgiou who was also competing in Anagennisi, was forced to stay out of action for a year.

Along the way he developed into one of the club's leading figures in the 1970s, with the highlight of his nine-year career at Aris winning the Greek Championship in 1979, captaining the team.

[4] Towards the end of his career, at the urging of Michalis Giannouzakos, he played for Iraklis, being one of the few basketball players who have worn the jersey of all three major teams of Thessaloniki.

[5] With the Greek National Youth Team, he won the silver medal at the 1970 FIBA U18 European Championship held in Athens.

[6] In the final, where Greece was defeated by a clearly superior Soviet Union 48–80 at the Panathenaic Stadium, Alexandris was the team's leading scorer with 12 points.

[9] His first European title came in 2001 when he coached Maroussi and won the FIBA Saporta Cup by defeating French side Élan Chalon 74–72 in the final held in Warsaw.