The Barclays Premier League outfit announced in a statement on Wednesday night that Cortese's resignation had been accepted and that their owner Katharina Liebherr had taken on the role of non-executive chairman, with the search having begun for a new chief executive officer.
Reports have suggested Cortese actually tendered his resignation earlier this season in the autumn and there was talk of the 45-year-old Italian considering his position back in May.
At that time, Pochettino warned he would leave Southampton if Cortese chose to do so.
The Argentinian manager, who was appointed as successor to Nigel Adkins in January 2013, said in May: ''I would not understand staying in this role if Nicola was not here.
''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.
''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."
Pochettino is scheduled to hold his regular pre-match press conference on Thursday afternoon ahead of ninth-placed Southampton's trip to Sunderland on Saturday.
Liebherr said in the statement on Wednesday: ''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.''
She also said Cortese's resignation had been accepted "with great regret", that he had "done a wonderful job" and that Southampton "very much wanted him to stay."
He took up the position in August 2009 after being instrumental in the purchase of the club that year by German-born Swiss businessman Markus Liebherr, and has since overseen the Saints' remarkable rise from League One to the top flight.
It is understood he had been contemplating quitting due to divisions between him and Katharina Liebherr - who became the club's owner after the death of her father Markus in 2010 - over future plans for the south coast outfit.
Southampton defender Luke Shaw, a reported target for a number of major Premier League clubs, 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!''
Having entered administration just prior to the Liebherr takeover, Southampton began 2009/10 with a 10-point deduction but soon rose from the bottom of the third tier, achieving back-to-back promotions in 2011 and 2012 under Adkins, brought in as a replacement for Alan Pardew.
And after the controversial sacking of Adkins, Pochettino led the Saints to a 14th-placed finish last term, with Southampton ending their comeback top-flight campaign five points clear of the relegation zone.
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- Nigel Adkins
- Nicola Cortese