The 46-year-old, who has had spells coaching Brondby, Getafe and Spartak Moscow, comes in to replace Gregorio Manzano who left at the end of last season.
Manzano led the side to a surprise fifth-placed finish in La Liga, just missing out on a place in the Champions League qualification round on the last day of the season.
Mallorca are struggling with debts of up to 85 million euros, are in administration, and have just been taken over by a consortium led by a former coach Llorenc Serra Ferrer.
Local media have speculated that the club's UEFA licence to be able to compete in the Europa League next season could be revoked due to their problems, but Laudrup played it down.
"It is a delicate moment to speak about economic matters," he told a news conference.
"I don't see why Mallorca has to be excluded from the Europa League. I expect to be playing the knockout rounds on August 19 and 26."
Laudrup led modest Getafe to a King's Cup final and to the quarter-finals of the UEFA Cup in 2008, where they lost in extra-time to Bayern Munich.
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