The contract incorporates the weekly title, which has a run-length of 70,000 and is printed in two 72-page sections.
BGP will print its first run of the magazine, which moves from Wyndeham Peterborough, for the 22 August issue.
Time Out's production manager Brendan McKeown said: "We have been able to be more bullish than we have been in recent years, more selective over a number of issues. Price is obviously one of them, but there are others."
BGP chief executive David Holland said: "The decision was based on the suitability of our manufacturing facilities and the Time Out management’s buy in to our long-term business plan and stability in a time of market discontinuity.
"We are very excited to be awarded such a prestigious title and it is definitely another brick in the wall so far as our growing contract business is concerned."