The publisher follows fellow media companies Bauer, IPC Media and Hachette Filipacchi, which have already launched digital versions of their titles on the newsagent's website, magazinesondemand.co.uk.
To raise consumer awareness of the roll-out, NatMag has tied up with The Telegraph to launch a three-month promotion, offering the newspaper's readers free access to the digital magazines.
From 25 March, readers of Telegraph.co.uk will be able to choose three free down-loads from 16 NatMag titles including Cosmopolitan, Men's Health, Good Housekeeping, Harper's Bazaar and Esquire. The company has a portfolio of 20 titles.
Readers who sign up for the promotion will receive their selected digital magazines via the John Menzies Digital platform, which is a joint venture between John Menzies and French media company Largardere Services.
John Menzies Digital said readers of online news sites, such as Telegraph.co.uk, were more likely to prefer access to magazines in a digital format.
NatMag announced last month it would shed 15% of its UK workforce to cut costs.