Clark replaces Stan Ternent, sacked by Hoyle on November 4 after just six months in the job.
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But director of football development Gerry Murphy will stay in caretaker charge for Saturday's Coca-Cola League One clash at Southend.
Chairman-elect Dean Hoyle: "I cannot stress enough the importance of the managerial team.
"Lee is the leader, but he's only as good as his coaching staff and I'm delighted he is backed up by a duo that has worked at the pinnacle of their respective professions.
"Derek Fazackerley has worked in the Champions League, Premiership and for the England national team and has a level of experience and knowledge comparable with any other coach in England today and he will be instrumental as assistant manager alongside Lee."