The Frenchman has signed a three-year contract and will have former Aston Villa coach Eric Black as assistant.
Pascal Plancque has also joined Puel’s backroom staff, while Southampton have agreed a deal to retain Dave Watson among the coaching set-up though Sammy Lee has left.
Les Reed, Saints’ executive director of football, said: “Claude clearly came out on top of a very impressive shortlist. We have not only got the best man, but the right coaching team to support him.
“To ensure we appointed a manager who would meet our needs as a club, feedback from the dressing room, as well as taking account of our culture, vision and values was critical in drawing up our criteria for the appointment.”
Puel made more than 500 appearances for Monaco before turning to management in 1999 after 17 seasons on the club’s playing staff.
Six seasons with Lille followed after he had led Monaco to the Ligue 1 title in 2000, while Puel also enjoyed a spell at Lyon in 2008 before four years in charge of Nice.
The Frenchman must now quickly reshape Saints’ squad after the departures of Sadio Mane and Victor Wanyama to Liverpool and Tottenham respectively.
Reed hailed Southampton’s new set-up by insisting former Villa coach Black can help underpin Puel’s tenure.
“Eric Black has an excellent pedigree as a coach and vast experience domestically and internationally,” said Reed.
“Pascal Plancque has an excellent record as a technical coach and, like Claude, has been responsible for developing many young French talents into top quality players.
“We have an excellent group of first-team players who are keen to take another step forward.
“There is already a confidence and excitement in the building as some of the squad has returned for testing and they are in great shape.
“Claude has a fantastic platform to work from and is aware that our ambition is to repeat and improve on our performances in the Premier League over the past three seasons.
“Claude has a track record of improving the situations he has been presented with and we are confident he can repeat this at Southampton.
“His Champions League and European experience will be valuable in our Europa League challenge this coming season and with the support of our excellent staff at the club I am sure he will do well.
“We are once again excited about what the new season will bring, and we will continue to chase records as we have done in recent years.”