Vasilogiannis was born in Patra Greece and started his career at local club Dyni Achaia, from where he was transferred to the youth academies of Olympiacos in May 2007. He made his official debut with the first team at the 2007 Greek Super Cup, coming as a substitute for Leonel Núñez in the 77th minute.
In August 2010, Vasilogiannis moved to Football League side Ethnikos Piraeus on a season-long loan. He made 22 appearances in the 2010–11 Football League, scoring 3 goals.
On 31 August 2011, Vasilogiannis was loaned out to Cypriot First Division side Apollon Limassol for a year. However, he never featured in the plans of his manager, Mihai Stoichiță, and he was released in late December of the same year, having failed to make a single first team appearance for the club.
In January 2012, just a few weeks after his return to Olympiacos, Football League 2 side Glyfada offered to sign him on loan until the end of the season, an offer which Olympiacos accepted as the player would not get any playing time there.
On 5 July 2012, Vasilogiannis moved to Kerkyra FC in the Superleague for a one-year loan. He made his Superleague debut on 16 September 2012, in a home match against Skoda Xanthi.
On 29 August 2013, he released his contect with Olympiakos joining the newly promoted Football League club Chania. On 9 July 2014, after a successful year (33 appearances, 2 goals, 5 assists) in Football League, he joined Lamia in a year contract for an undisclosed fee.
On 8 July 2015, Vasilogiannis agreed to continue his career with Cypriot First Division club Ermis Aradippou, following his former coach, Pavlos Dermitzakis. He signed a year contract (plus one more) for an undisclosed fee.
On 16 June 2016, Vasilogiannis returned to his former club Lamia in order to help with his experience to fulfill the club's goal to be promoted to Super League.
On 4 July 2017, Vasilogiannis signed a three years contract with TFF First League club Ümraniyespor for an undisclosed fee.