(Chris Rank/ Bloomberg News)

AT&T will start selling unlimited data plans again, the company said Monday.

The new offering, which begins Tuesday, allows customers who sign up for the plan to use as much data, voice and text messaging as they want. And it marks the return of a feature that AT&T stopped offering to new customers years ago.

But the resurrection of unlimited data comes with a twist: Consumers will only be eligible for the plan if they also agree to subscribe to one of AT&T's paid television services — either DirecTV or AT&T U-verse.

The decision to bundle wireless service and pay-TV with unlimited data reflects AT&T's desire to get consumers streaming more TV on their smartphones. Telecom companies are searching for new ways to make their mobile networks attractive to consumers, and with the exploding popularity of online video, particularly on handheld devices, AT&T hopes it can lure more Americans into using its network.

The new plan is being aimed squarely at AT&T customers who have either phone service or TV service, but not both, AT&T execs told CNN. Altogether, that's 36 million households.

Expanding into TV is also key for wireless companies as the cellular market has gotten increasingly competitive, with carriers engaging in costly price wars just to poach customers from rival services, analysts have said.