The former Denmark midfielder had been out of work since being sacked by Premier League side Swansea City in February, but has signed a one-year deal with Lekhwiya.
Laudrup last month ruled out taking over at "smaller clubs" of the same stature as his previous employers Swansea, Getafe and Mallorca.
And he has now opted to ply his trade in the Middle East.
He told Danish newspaper Politiken: "I'm heading into my last phase as a coach. But whether Lekhwiya will be my last or second-last team remains to be seen.
"And I don't know it the phase will stretch over two, three or four years. The answer is blowing in the wind."
Laudrup won Swansea's only major trophy in his first season in charge, but was relieved of his duties just a year later.
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