Lynn, who will take up the role in the next few weeks and report to president Bob Bakish, will replace Michiel Bakker, who announced he was leaving last week.
He will continue to oversee Nickelodeon until a successor is appointed.
MTV has also promoted managing director of music and comedy Heather Jones to the new role of executive vice president of content and creative, overseeing its multi-platform content and brand strategy for music and comedy.
Lynn will be responsible for all MTV Network's UK operations, including 17 TV channels, 16 web sites and mobile TV channels spanning its MTV, MTV Flux, VH1, and TMF brands, as well as its interests in its joint venture businesses with BSkyB such as Nickelodeon UK and Paramount Comedy Channel UK.
MTV parent company Viacom announced last week that it would make 250 redundancies in the UK, Latin America and emerging markets.