The fifth-tier English side announced the news on their website on Saturday morning (AEST).
Bouzanis played 15 games for Melbourne City this season, before deciding to leave the club to join his partner, Matildas defender Steph Catley, in London.
Catley has recently signed for Arsenal, and Sutton United's base is close by in South London.
Sutton United finished 15th last season in the National League.
It will be a return to England for Bouzanis who started his career at Premier League giants Liverpool, but never broke through to the first team.
He had spells at Accrington Stanley and Oldham Athletic in the lower divisions, before heading to Greece where he signed for Aris.
In 2014, Bouzanis returned to Australia, signing for Western Sydney Wanderers.
Two years later he signed for Melbourne City.