Cortese, who took on his role at St Mary's Stadium in August 2009 and reportedly considered leaving at the end of last season, is thought to have resigned due to differences in opinion with owner Katharina Liebherr over short and long-term planning at the club.
Liebherr will assume Cortese's role ahead of the appointment of a full-time replacement.
A Southampton statement read: "Southampton FC announces that club owner Katharina Liebherr has taken on the role of non-executive chairman.
"This follows the resignation of Nicola Cortese. A search has begun for a chief executive officer."
Liebherr added: "With great regret we have accepted the resignation of Mr Cortese.
"He (Cortese) has done a wonderful job and we very much wanted him to stay. A search has now begun for a successor.
"It is business as usual and we will ensure that the manager, team and staff at the club have all the help and support they need."
Cortese was a key factor in the appointment of Pochettino as Nigel Adkins' replacement last January, and the Argentine coach has previously said his future at Southampton was dependent on whether or not the Italian remains.
When asked in May if he would stay at Southampton in the event of Cortese's departure, Pochettino said: "Of course not because the person that has put faith in me in this club and as a manager is Nicola Cortese."
Southampton sit ninth in the Premier League, with 30 points from 21 games this term.
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