Christiansen led APOEL Nicosia to the Cypriot league title earlier this year and the last 16 of the Europa League for the first time in the club's history.
The 44-year-old also spent a short time as assistant manager at Abu Dhabi-based club Al Jazira under Luis Milla in 2013, before taking over AEK Larnaca in 2014.
“Thomas was someone who had been on our radar from the very early stages of the process and quickly established himself as the outstanding candidate," Leeds United managing director Angus Kinnear said in a statement.
"We are confident we have found a man with who can work with us to take the club to the next level.”
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Leeds, who finished seventh in the second-tier Championship, are one of the fallen giants of the English game, having won the top-flight title on three occasions and finishing as runners-up in the 1975 European Cup.
The Yorkshire club have struggled on and off the pitch since losing their Premier League status in 2004.
(Reporting by Hardik Vyas in Bengaluru; editing by Mark Heinrich)
