The three previously worked together at Newcastle United when Clark, 36, was a player under Kevin Keegan.
After ending his playing career, Clark later joined the coaching staff at St James' Park under Glenn Roeder, before linking up with him again at Norwich City.
For Clark, who is currently completing his Uefa Pro Licence, the Hudderfield job is his first chance as a manager.
Hoyle said: "People have to understand that although we have enjoyed some short-term success, it is fair to say that the last 20 years have not gone according to plan for Huddersfield Town.
"We needed to try something different with this managerial appointment as opting for experience has not worked.
"Every manager who is highly regarded in football today needed a break somewhere to get his career underway and I firmly believe that Lee is the man we were looking for.
"He definitely embraces what we want to achieve here at Huddersfield Town. I was looking for a young and innovative manager and he is very keen on the implementation of new ideas and techniques.
Clark's rise to manager
2005 - Fulham captain
2006 - Newcastle reserve team coach
2007 - Norwich assistant manager
2008 - Huddersfield manager
"Lee played a good, quick passing style of football throughout his playing career and he will carry that into management - that is how he wants his team to play.
"He also wants his team to be as fit and as organised as possible."
Clark will be the club's fourth manager in the space of two years following Peter Jackson, Andy Ritchie and Stan Ternent, who was sacked in early November.
And his former boss at Norwich, Roeder, wished Clark well in his new post at the Galpharm Stadium.
"I always knew from day one when I first appointed Lee as reserve team coach at Newcastle how ambitious he was to become a manager one day, probably sooner rather than later," Roeder told Norwich's website.
"At that stage he was just completing his A licence and today he's just about to complete his Pro Licence, which he's been doing with the Northern Ireland FA.
"I just want to say I truly hope Lee goes on to fulfil his ultimate ambition by one day managing Newcastle United, any Geordie's dream."
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