The 48-year-old former Barcelona and Real Madrid midfielder replaces Brendan Rodgers, who left the club to take over at Liverpool at the start of the month.
A club statement confirmed: "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."
Laudrup won five Spanish league titles in the early 1990s, four of them with Barcelona as part of Johann Cruyff's dream team.
He was capped 104 times for Denmark.
As a manager he has had spells with Brondby, Getafe, Spartak Moscow and Mallorca.
Rodgers left for Anfield on June 1 after a two-year stint with Swansea that saw him steer the Welsh club to promotion to the Premier League and secure their top-flight status with an impressive 11th-place finish last term.
Source: AFP
Source: AFP