Galitsios started playing with the team's youth squad, in June 2008.
After having several successful appearances in the U-21 championship, he was promoted to the first team in January 2012, having signed a 4,5-years contract.
He made his professional debut on 9 May 2012, against Panthrakikos, under manager Michalis Ziogas.
He made his international U-19 debut on 3 September 2011, on a friendly match against Sweden.
He is the youngest son of the team's former captain and all-time appearances record holder Giannis Galitsios, and brother of Giorgos Galitsios, who has also played in the team for several years and is now playing for Cypriot club Anorthosis.