Pochettino, who has signed a five-year contact, had been widely tipped to succeed Tim Sherwood after guiding Southampton to their highest-ever Premier League finish of eighth place last season.
After joining Southampton following the sacking of Nigel Adkins in January 2013, Pochettino also helped develop home-grown talent such as the England pair of Luke Shaw and Adam Lallana.
Tottenham chairman Daniel Levy told the club's website: "In Mauricio I believe we have a head coach who, with his high energy, attacking football, will embrace the style of play we associate with our club.
"He has a proven ability to develop each player as an individual, whilst building great team spirit and a winning mentality.
"We have a talented squad that Mauricio is excited to be coaching next season."
Pochettino added: "This is a club with tremendous history and prestige and I am honoured to have been given this opportunity to be its head coach.
"There is an abundance of top-class talent at the club and I am looking forward to starting work with the squad.
"Tottenham Hotspur has a huge following across the world and I have great admiration for the passion the fans show for this team.
"We are determined to give the supporters the kind of attacking football and success that we are all looking to achieve."
Southampton chairman Ralph Krueger has pledged to continue to develop the club and said the search for a new manager has already started.
Krueger said: "The club has been on a constant path of growth since the arrival of Markus Liebherr in 2009.
"This growth took place before Mauricio came, it continued strongly under his leadership, and it will continue into the next season. The board's job is to find opportunity in this challenge and to continue to move the club forward.
"We have begun the search for a new high-calibre manager.
"We will be looking for a manager that shares our values, our principles and our philosophy; a manager who can continue to grow the first team and build on our strong foundation - a foundation led by an ambitious vision and plan that continues to build on our world-class academy, our amazing 129-year heritage and our excellent staff, and rewards our loyal and passionate fan base."
Pochettino has also taken his back-room staff to White Hart Lane with Jesus Perez (assistant head coach), Miguel D'Agostino (first team coach) and Toni Jimenez (goalkeeping coach) all following him to north London.
"There is an abundance of top-class talent at the club...or so Levy and Baldini keep telling me. I look forward for their using this delusion as a stick to beat me with when I am fired within two years for not massively overachieving."- dr soccer