The customer title has the widest circulation in the UK, with an ABC of 6.8 million.
John Brown had also pitched for two new titles, Sky Movies and Sky Sports, but these contracts were awarded to Future and Haymarket respectively. The Sky contract accounted for around 20% of the publisher's total business.
Andrew Hirsch, chief executive, said he hoped to find new positions for around 30 people affected by the move.
"When News International set up its magazine division, it clearly put us at risk, so we have been aware this might happen," he said. "But eight out of our top 10 clients have had double-digit growth this year and they're spending much more."
John Brown will continue to publish children's magazine Sky Kids, which is sent monthly to 800,000 targeted Sky households and its accompanying website.
John Brown had published the title since winning the contract from Redwood in 2002. Conde Nast had also been in the running, but was ruled out earlier this month.
The title is sent directly to Sky subscribers' homes and has an ABC of 6,798,945.
News Magazines is expected to make it more entertainment-focused to complement the new film and sports titles.
Sky is also understood to be planning a further magazine targeting what it calls ABC1 'cultural connoisseurs'. Sky said in a statement that it might consider further segmentation in due course.