Burch will replace outgoing chief executive Simon Duffy, who is moving to the position of executive vice-chairman, on January 16.
Duffy, who joined NTL in 2003, will be responsible for the company's strategy and business development.
Burch, who is currently president of Comcast's Atlantic division, has spent 17 years at the company in various roles. He was a key player in Comcast's acquisition of AT&T Broadband for $72bn in 2001.
As such, his experience in mergers should stand him in good stead to complete the Telewest deal and proposed acquisition of Virgin Mobile.
NTL is in bid talks with Sir Richard Branson's Virgin Mobile, which would allow the cable giant to take on Sky by rebranding as Virgin Media and offering mobile calls as well as TV, broadband and fixed-line calls.
Last week, Virgin shareholders rejected bids of £817m, but Branson is prepared to accept less for his 72% stake in the company, giving minority independent directors more, so that NTL will go ahead with the takeover.
In addition, the cable giant also revealed it was amending details of the Telewest merger, in effect making it an acquisition, so the combined companies can keep the UKTV contract with the BBC, which owns a 50% stake in the 10 channels.
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