He became a regular member of the team in 2002–03 season and stayed to APOEL until the summer of 2006, playing in total 103 matches and scoring 24 goals.
Alexandrou was considered one of the most important players for Larissa after the team returned to the Super League Greece.
He also appeared in six 2011–12 UEFA Champions League matches for APOEL, in the club's surprising run to the quarter-finals of the competition, including the round-of-16 triumph over Olympique Lyonnais where he converted his attempt in the penalty shootout.
[8][9] Alexandrou made his only group stage appearance in APOEL's 2014–15 UEFA Champions League campaign on 10 December 2014, playing the full 90 minutes in his team's 4–0 defeat against Ajax at Amsterdam Arena.
[11] After the end of the 2015–16 season, in which he crowned champion for a fourth time in the row, Alexandrou signed a new one-year contract extension with APOEL, becoming also the team's captain.
On 11 September 2014 Alexandrou married with Cypriot tv presenter and former model Constantina Evripidou in Mykonos.