The magazine will play a key role in Virgin Media's effort to regain consumer confidence after its public spat with BSkyB and the loss of several Sky channels.
It will be the first dedicated magazine for customers of a rival platform to Sky.
Virgin Media has spent £20m on the rebrand of the former ntl:Telewest, including a high-profile TV and press campaign featuring Kill Bill star Uma Thurman.
James Kydd, Virgin Media's managing director of marketing, said he was exploring several publishing opportunities with Redwood, but Virgin would take a different path to its rival. "It is extremely unlikely that we will use the Sky approach to market as a benchmark," he said.
Redwood beat Square One and John Brown, which recently lost the contract to publish Sky's magazine to News Magazines, to the deal.
Brian Whittaker, the former group publisher for home interest titles at BBC Magazines who previously published Age Concern's Heyday magazine for Redwood, will lead the publishing strategy.
BBC Magazines already produces an edition of the Radio Times promoting Virgin Media's listings for the broadcaster's subscribers, a promotional tactic that was inherited from NTL.
Sky: The Magazine, which News Magazines will publish from the summer, is distributed to 7,002,232 customers, the highest circulation of any UK magazine.
BSkyB recently increased its communication to customers with the launch of magazines for subscribers to its premium film and sports packages, published by Future and Haymarket respectively.