Nigel Adkins has been sacked as manager of Saints and replaced by former Espanyol coach Mauricio Pochettino.
Adkins was nearly fired earlier in the season, after a 2-0 loss at West Brom in November left them bottom of the table.
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However, following that defeat he had masterminded an impressive upturn in fortunes, with Saints losing just two of their last 12 Premier League matches and pulling three points clear of the drop zone.
That was not enough to stop Cortese putting his search for a new boss on hold, however.
Reports emerged in the last 24 hours that the St Mary’s chief had met Argentinian coach Pochettino, who has been out of work since late November, when he was let go by Espanyol after a poor run of results.
The 40-year-old former Argentina international took over at the Spanish club in 2009, marking his first job in management.
A statement from Cortese said: "This decision has been made with the long-term ambitions of Southampton Football Club in mind. Whilst we acknowledge the contribution Nigel has made during the past two years, for the Club to progress and achieve our long-term targets a change was needed.
“Mauricio is a well-respected coach of substantial quality who has gained a reputation as an astute tactician and excellent man manager. I have every confidence that he will inspire our talented squad of players to perform at the highest possible level.
“He also shares my belief that the most successful clubs are built by nurturing young players through a development system that provides a clear path to the First Team, thereby creating a culture that keeps them at the Club for the long term. This is an approach he has employed with great success in the past and I look forward to him bringing that experience and expertise to Southampton.”
A comment from Pochettino added: “This is the kind of opportunity that any coach would relish. Southampton is a club with great heritage, and an even more exciting future. There is a clear vision to take the Club to a new era of sustained success in the Premier League, and beyond, which I’m delighted to be part of.”