In a statement, the Barclays Premier League outfit announced club owner Katharina Liebherr had taken on the role of non-executive chairman following Cortese's resignation.
They also said a search had begun for a chief executive officer, who will take over Cortese's executive duties.
Liebherr said in the statement on Southampton's official website: ''With great regret we have accepted the resignation of Mr Cortese.
''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.''
Yet there was talk of Cortese considering his position in May, and at the time Pochettino warned he too would leave Southampton if his boss chose to do so.
The Argentinian manager, who was appointed as successor to Nigel Adkins in January 2013, said last year: ''I would not understand staying in this role if Nicola was not here.
''The person that actually called me from the start, told me about the project and put their faith in me was Nicola.
''I have great respect as well for Southampton, the club and the supporters, but Nicola has been the one that has placed his trust and faith in me.
''I wouldn't see myself in this club if it was not for him. We are on the same wavelength about the club and the future of the club so it really would not make any sense if I was at this club and he was not."
Southampton are currently ninth in the table.
Defender Luke Shaw gave his reaction to Cortese's departure in a message on Twitter, writing: "Gutted with that news, but would just like to thank Nicola Cortese for everything he has done for me and the club! All the best to him!"
Italian Cortese was appointed as Southampton's executive chairman in 2009 after being instrumental in German-born Swiss businessman Markus Liebherr's purchase of the club earlier that year, and has since overseen their remarkable rise from League One to the top flight.
It is understood Cortese had been contemplating quitting due to divisions between him and Katharina Liebherr, who took over as the south coast side's owner following the death of her father Markus in 2010.
Pochettino is scheduled to hold his regular pre-match press conference on Thursday afternoon ahead of Southampton's trip to Sunderland on Saturday.
There have been reports claiming 45-year-old Cortese first handed in his resignation several weeks ago.
His reasons are unclear, however Liebherr is planning to sell the club according to the BBC.
Having entered administration just prior to the Liebherr takeover, Southampton began Cortese's first season as executive chairman with a 10-point deduction but soon rose from the bottom of the third tier.
They achieved back-to-back promotions in 2011 and 2012 as Adkins, brought in as a replacement for Alan Pardew, guided them to the Championship and then Premier League.
And after the controversial sacking of Adkins, Pochettino led the Saints to a 14th-placed finish last term, with them ending their comeback top-flight campaign five points clear of the relegation zone.