Moschonas began playing professional football with AEK Athens in 2009.
[1] On 1 January 2010, he was loaned to Elpidoforos for the rest of the season.
In 2013, AEK were relegated and Moschonas left the club on a free transfer.
On 7 August 2013, he signed for newly promoted Fostiras in the Football League.
[2] In July 2014, he signed for Levadiakos in the Super League.