Laudrup replaces Brendan Rodgers who joined Liverpool earlier this month.
The former Brondby, Getafe, Spartak Moscow and Real Mallorca boss has penned a two-year-deal with the Welsh club.
Swansea City statement: "Swansea City are pleased to confirm the appointment of Michael Laudrup as the club's new manager.
"Contracts were completed at noon today on a two-year deal."