The south coast club confirmed Cortese's resignation, with Saints co-owner Katharina Liebherr installed as non-executive chairman.
"With great regret we have accepted the resignation of Mr Cortese," Liebherr said in a statement.
"He 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."
The BBC reported that Cortese had actually proffered his resignation a few months ago and was merely serving out his notice period.
The 45-year-old Italian banker, who became the Saints' executive chairman in 2009, has suffered an "irretrievable breakdown" in relations with club owners the Liebherr estate, according to the Southern Daily Echo.
Cortese's exit throws the club into turmoil, as manager Mauricio Pochettino - who has been credited with turning the side into a credible force in the Premier League - is widely expected to leave.
Pochettino said last year that he would only remain at St Mary's as long as Cortese retained his post.
Cortese's future had been the subject of speculation last summer before an interim agreement between him and Liebherr estate over the direction of the club as well as his contract.
But, the Echo reported, discussions since then to agree a long-term strategy have not produced a solution, and Cortese has now apparently left.
Cortese persuaded German-born industrialist Markus Liebherr to buy the club in 2009, when Saints were in administration and playing in the third tier. Liebherr died in August 2010, when ownership of the south-coast club passed to his family estate.
Cortese ran the club's day-to-day affairs as Southampton climbed from League One to the Premier League in three years.
His most controversial act was to sack manager Nigel Adkins in January 2013 and replace him with Pochettino.
Fans were highly critical of the change and the treatment of Adkins but former defender Pochettino won them round, ensuring Southampton retained their top flight status last term with wins over Manchester City, Liverpool and Chelsea along the way.
Cortese was also a shrewd operator in the transfer market, backing his managers to bring in now-established players such as Rickie Lambert, Jay Rodriguez, Victor Wanyama, Dejan Lovren and Dani Osvaldo, who arrived from AS Roma in August 2013 for a club-record fee of £15 million.