Called the “Netflix of magazines”, Texture offers US-based users unlimited access to more than 200 titles for a monthly fee of $9.99 (£7.19).
It is currently owned by Next Issue Media, which is backed by magazine publishers Conde Nast, Hearst, Meredith, News Corp, Rogers Communications, and Time.
Apple said it was “committed to quality journalism from trusted sources”.
“We’re excited Texture will join Apple, along with an impressive catalog of magazines from many of the world’s leading publishers,” said Eddy Cue, Apple’s Senior Vice President of Internet Software and Services.
Texture offers access to magazines like The New Yorker, People, Time and GQ.
Texture was launched in 2010 and won a “Best Of” award from the App Store editorial team in 2016.
Apple already runs a music-streaming subscription service and has been commissioning new television content, leading to speculation that it might launch a rival to Netflix.