The former Espanyol boss has replaced Nigel Adkins, prompting widespread disbelief and anger amongst fans and ex-players, who feel Adkins - the man who won back-to-back promotions - has been harshly treated.
Pochettino said: "I am very happy to be here in this amazing weather. It happened quickly, small details are not important, it's important I'm here at this project and club.
"They have done really well in the Premiership. In Spain we follow it closely. I am a great admirer of English football and am happy to be here.
"The challenge is to be part of this project, the kindness of the supporters is the biggest challenge I have," he said at a news conference.
"They are the biggest part of this club and I hope I can convince them with honest and hard work.
"I am very passionate about the Premier League. I have seen many games, the Premier League is an attractive league and I have spoken to people at length about it, people such as Jose Mourinho, who is a good friend of mine.
"He told me the best football in the world is being played here."
In making the decision, executive chairman Nicola Cortese said he was looking at the long-term future of the club.
The Saints drew 2-2 at European champions Chelsea on Wednesday night - a considerable feat seeing as they were in the League One relegation zone when Adkins took the job in September 2010.
"This decision has been made with the long-term ambitions of Southampton Football Club in mind," said Cortese in a statement.
"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."
Pochettino's first game in charge will be Monday night's clash with Everton.
The fans are likely to at least show support for Adkins but, according to former Southampton star Matt Le Tissier, they should not be surprised at what has happened.
"It doesn't surprise me," he told Sky Sports News. "It's a strange time of the season, they've lost two of the last 12 games and came from 2-0 down to draw at Chelsea.
"(But) it seems to be the way the club's being run under the chairman. Nothing's surprising and it's a bit of a laughing stock."
The ex-England international did concede the timing shocked him - Saints have been in good form and are clear of relegation trouble at present - but added he felt this could have been on the cards for some time.
"I'm shocked at the timing, it's very strange and it's an odd thing to come to terms with today," he said.
"I think he had a bit of pressure early on this season, people thought it might happen then; maybe they couldn't get the man they wanted then. It's all very strange."