Sunday is thought to have won out in a competitive pitch against other customer publishers, including Seven. Sky Magazine was previously published in-house.
Sky Magazine is the largest circulation magazine in the country with an average net distribution of 7.3 million. The quarterly title includes a programme guide and celebrity interviews, and is distributed free of charge to Sky customers.
Sunday is expected to publish its first issue of the quarterly in September. It was previously published monthly.
Earlier this year Sky decided to dramatically scale back its customer magazine output, closing Sky Sports Magazine and Sky Movies Magazine, which will live on as weekly emails published in-house.
The win marks a coup for Sunday, which is outside the big league of customers publishers such as John Brown Media Group, Redwood and Publicis Blueprint.
Sunday reported revenues of £3.7m in 2010 and employs just 28 people. It publishes titles for brands including Toyota and Vodafone.
It is unclear whether the move will lead to job cuts at Sky.
Sky and Sunday were unavailable for comment.