The former Denmark international has been named as successor to Brendan Rodgers, who joined Liverpool earlier this month.
Laudrup won five Spanish league titles with Barcelona and Real Madrid in the early 1990s and the creative midfielder was one of the players of his generation.
However, the 47-year-old had spells in charge of Brondby, Getafe, Spartak Moscow and Real Mallorca which failed to deliver any prolonged success.
Laudrup, though, will do plenty of research on the job in front of him as he prepares to tackle the English top flight.
"It is going to be a new experience for me and I am really looking forward to it," he said.
"I have spoken to many people about Swansea and watched a number of their games on DVD - with many more to watch.
"Everyone knows the style of football Swansea play and it suits my way of thinking."
Swansea chairman Huw Jenkins played his cards close to his chest in the search for a new boss at the Liberty Stadium.
A number of names were linked with the vacancy - including Gus Poyet, Marcel Desailly, Dennis Bergkamp and Wigan assistant manager Graeme Jones.
Jenkins is confident the Dane can have a major impact on the Barclays Premier League.
"There is no doubt about his standing as one of the game's greatest footballers, but we also see the qualities he has as a manager," the Swansea chairman said.
"We see Michael as someone who is fully committed and educated in all aspects of the way we want to take the club forward.
"Our overall aim is to build on our first season in the Premier League, but we also fully understand the need to adapt our approach as we go along to remain competitive season after season.
"Part of that process is to look at new ideas and increase our knowledge on all aspects of the game to keep advancing.
"Everyone I've spoken to about Michael during the appointment process can't speak highly enough about him, not just as a football man, but as a person.
"I am confident that Michael will prove a fantastic acquisition that will help keep this football club moving forward."
Laudrup will head to Swansea towards the end of next week as preparations begin for pre-season, and confirmation over his backroom staff will follow.
Swansea have tied up midfielder Lee Lucas, 20, on a new three-year contract, but it remains to be seen whether a proposed £6.8million deal for the permanent signing of Gylfi Sigurdsson from Hoffenheim following a successful loan spell will be completed.
It has been suggested the Icelander could now instead link up with Rodgers at Anfield.
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