Apple didn't say how much it would pay for Texture, which gives users digital access to 200 magazines for one monthly fee.
But the acquisition is another step for Apple to build out its software and services business with recurring subscription revenue, as it competes with companies like Amazon, Facebook and Google, which are increasingly combining hardware and software. Facebook and Google, in particular, have been under scrutiny for the way that their services present news content.
"We are committed to quality journalism from trusted sources and allowing magazines to keep producing beautifully designed and engaging stories for users," Eddy Cue, Apple's senior vice president of software and services, said in a statement.
At a SXSW conference panel on Monday, Cue said he wanted Apple to avoid "the issues going around the marketplace."
"We're not after trying to keep getting you to read the same thing over and over again to sell ads," Cue said. "For ourselves, when we got into this we thought when you have a large platform there's a lot of responsibility — and we've always taken a great deal of responsibility for our platforms."
— CNBC's Michelle Castillo contributed to this report.