Puel becomes the Foxes' third manager this year, replacing Craig Shakespeare who succeeded Premier League title winner Claudio Ranieri in February.
Puel, 56, led the Saints to eighth in his first season in charge, as well as reaching the EFL Cup final, but the Frenchman was sacked in June.
Michael Appleton will remain as Leicester's assistant manager.
Appleton had taken caretaker charge after Shakespeare was sacked just four months after he signed a three-year deal to take the job on a permanent basis.
Leicester City vice-chairman Aiyawatt Srivaddhanaprabha said Puel was "a perfect fit".
"Upon meeting Claude, his attention to detail, knowledge of our squad, understanding of our potential and his vision to help us realise it were extremely impressive," he added.
"He quickly emerged as the outstanding candidate and I am delighted we will have the opportunity to reinforce our long-term vision, aided significantly by his expertise."
Puel takes over a Foxes side 14th in the Premier League table with two wins from nine games.
The former Monaco boss, who has also had spells at Lille and Lyon, spent four years as manager of Nice before replacing Ronald Koeman at Southampton.
He said it was "a great privilege" to take over at Leicester, adding that the club's "values and ambitions are closely aligned to my own".
"The opportunity to help the club build on its remarkable recent achievements is a truly exciting one and I'm looking forward to working with the owners, players, staff and supporters to deliver further lasting success."
Despite losing 16 games last season, Puel led Southampton to an eighth-placed finish in the Premier League. Their 3-2 defeat by Manchester United in the EFL Cup final at Wembley was their first major final since 2003.
But he was dismissed after managing just one win from the final eight league matches of the season, with his side scoring just once in their last six games.
Phil McNulty, chief football writer
Leicester City's appointment of Claude Puel is not the arrival many expected when Craig Shakespeare was sacked - and will be regarded as an underwhelming appointment by many supporters.
Frenchman Puel was dismissed by Southampton at the end of last season after a campaign that looked good on paper but left many of the fans at St Mary's cold with his style of play.
The problem for Puel was his understated personality that did not create any bond with Southampton's supporters and tactics that became increasingly stodgy as the season progressed.
The Frenchman was not among anyone's considerations when Shakespeare left, but Leicester's board have looked at his highly respectable record at Monaco, Lille, Lyon and Nice.
He will still, however, have to make a fast start as many will still regard him as damaged goods after his sacking by Southampton and a departure that was not mourned.
Premier League records of Leicester's managers since the club's Thai owners took control
Manager Games Win %
Nigel Pearson 38 28.9
Claudio Ranieri 63 44.4
Craig Shakespeare 21 38.1
Leicester have kept Michael Appleton as assistant manager alongside Puel and he will be a valuable sounding board for the new boss.
And while the appointment will raise eyebrows and have plenty of questions fired in the direction of Leicester's owners, they will have an answer ready to those who will question their judgement.
They were met with a similar puzzled reaction when Claudio Ranieri was appointed as successor to Nigel Pearson in the summer of 2015.
It led to the most glorious season in the club's history as they won the Premier League title - and while no-one is expecting a similar outcome, it may be unwise to write off the somewhat left-field appointment of Puel too soon.