The 50-year-old Dane has been out of a job since leaving Swansea in February, just a year after winning the Capital One Cup.
Doha-based outfit Lekhwiya are the champions of Qatar and were previously coached by Belgian Eric Gerets.
The club said on their official website that details of his contract would be announced at a later date.
The former Barcelona and Real Madrid midfielder admitted he may look for a challenge beyond football management when his deal with Lekhwiya expires.
He told Danish newspaper Politiken: "I'm now entering my final phase as a coach.
"Although whether Lekhwiya will be my final or penultimate club I can't say.
"And I don't know either whether this phase while last two, three of four years. The answer is blowing in the wind."