Born in the village of Apiranthos (Aperathu), Naxos, Glezos moved to Athens in 1935 together with his family, where he finished high school.
On 30 May 1941 he and Apostolos Santas climbed on the Acropolis and tore down the swastika, which had been there since 27 April 1941, when the Nazi forces had entered Athens.