Clark replaces Stan Ternent, sacked by Hoyle on November 4 after just six months in the job.
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Clark has signed a three-and-a-half-year contract at the Galpharm Stadium and is joined by former Newcastle, Manchester City and England stalwart Derek Fazackerley and fitness coach Steve Black.
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."