Alexandrou was born on December 19, 1983. He played from 2000 until 2006 for APOEL Nicosia before moving to Greece and AE Larisa. At Larisa, Alexandrou won the Greek Football Cup in 2007. The following year, he returned to Cyprus and APOEL.
So far (July 2018), Alexandrou has been capped 40 times by the Cyprus National Football Team.