Katz leaves his role as director of content acquisition at Virgin Media after seven years in the business development division at the company, which was previously NTL/Telewest.
At Virgin, Katz was responsible for negotiating content deals and on demand and internet deals with broadcasters, studios and labels.
He succeeds Scott Monks and Dave Young at Box TV, who have run the business over the past 12 months as acting joint managing directors. They have been promoted to board level and will continue to be closely involved with the development of the music television venture.
Katz said: "With Channel 4 and Emap as shareholders we can establish Box TV as the outstanding music TV business in the UK, while developing commercial models and platforms to extend our interactions with the digital generation of music consumers."
Since the announcement of Channel 4's investment last year, the company has extended its carriage deal with Sky and seen The Hits channel named as one of the most watched music channels in the UK.
Rod Henwood, director of new-business at Channel 4, said: "Under their management [Monks and Young], the businesses share of music TV viewing has grown to record levels and I'm pleased that Gidon's expertise will complement their considerable skills and take the business to a new level."
Emap bought The Box in 1996 for £6m and has built up its music TV business through a series of successful launches.
It now comprises seven TV channels: The Hits, The Box, Smash Hits, Kerrang!, Q, Kiss and Magic.
Channel 4 acquired its 50% stake in the business in July 2007 for £28m.