Luzon replaces Rene Meulensteen who was fired after just six months at the helm.
Luzon left Hapoel Tel Aviv last month after the club went into administration. Commenting on his new role at Haifa, he said: "This is a wonderful challenge and the summit of my career so far."
Meulensteen, who served as assistant coach to Sir Alex Ferguson at Manchester United for five years, has failed to turn around the fortunes of the Ligat Ha'Al outfit. Haifa are in seventh place, trailing 20 points behind leaders Hapoel Beer Sheva.
Commenting on his departure, Meulensteen said: "I felt I was sinking in quicksand and the players were not on my side. It's sad to leave but my time in Israel has been a marvelous chapter in my life."
Maccabi chairman Jacob Shahar commented: "At every club when the results are disappointing the time comes for a change."
There has been a spate of managerial changes at Israel's top clubs over the past week. Maccabi Tel Aviv has appointed former Angola national team manager Lito Vidigal to replace the Georgian Shota Arveladze who was departed in December. Beitar Jerusalem has appointed Sharon Mimer as manager after sacking Ran Ben-Shimon.
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