Stockwell, who was previously brand marketing director of the Virgin Group, has worked for the Virgin Group for the past 17 years, starting at Virgin Atlantic.
He has also worked at various group companies including Virgin Cinemas, Virgin Drinks, Virgin Trains and Virgin.com.
Stockwell said: "I'm absolutely delighted to be joining the team and to build on the great work that has been done since the launch of Virgin Media.
"We have already achieved significant resonance with British consumers and now there is an enormous opportunity to capitalise on this with more hard hitting, innovative campaigns."
Kydd left Virgin last month to take a career break.
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