NEW YORK — Verizon Wireless, the nation’s largest cellphone company, is phasing out nearly all of its existing phone plans and replacing them with pricing schemes that encourage customers to connect their non-phone devices, like tablets and PCs, to the Verizon network.

The revamped plans let families and other subscribers share a monthly data allowance over as many as 10 devices – the biggest overhaul in the price of wireless service since the cellphone became a mainstream device. The idea is likely to be copied quickly, at least by AT&T Inc., which has already said it is considering introducing shared-data plans soon.

Verizon’s move “is the most profound change to pricing the telecom industry has seen in 20 years,” said Sanford Bernstein analyst Craig Moffett.

For Verizon, the approach reflects a desire to keep growing now that nearly every American already has a phone.

In the first quarter of this year, phone companies, for the first time, reported a drop in the number of phones on contract-based plans, which are the most lucrative. To keep service revenue rising, companies are betting on increased data usage, and that means getting more data-hungry devices on their networks.

Verizon’s new “Share Everything” plans, announced Tuesday, will become available June 28. They include unlimited calls and texts and will start at $90 per month for one smartphone and one gigabyte of data.

If used only with a smartphone, “Share Everything” prices are lower than for current plans with unlimited calling and texting, but higher than plans with limited calling and texting.

The plans will push many subscribers toward spending more by including unlimited calling and texting by default. Unlimited calling plans provide peace of mind, but not many people need them, and the average number of minutes used is declining.

From Verizon’s perspective, offering unlimited access is an efficient use of its network because calling and texting take up little capacity. Data usage, on the other hand, consumes a lot of network resources.

The savings will come to subscribers who add more devices to their plans. In such cases, the new pricing system will be cheaper compared with separate data plans for each device. Today, few consumers put tablets on data plans, probably because they dread paying an extra $30 or so per month, on top of their phone bills.

Under “Share Everything,” adding a tablet to a plan will cost $10 per month. Adding a USB data stick for a laptop will cost $20.

Verizon’s limited calling and texting plans will disappear, except for one $40-per-month plan intended for “dumb” phones. Verizon is keeping its limited-data plans for single non-phone devices, like the $30 tablet plan.

Current Verizon customers will be able to switch to the new plans or keep their old ones, with one exception. Those who have unlimited-data plans for their smartphones won’t be able to move those to new phones, unless they pay the full, unsubsidized price for those phones. (For example, an iPhone 4S that costs $200 with a two-year contract costs $650 unsubsidized, with no contract.)

Under the new plans, subscribers can stop worrying about monitoring the number of calling minutes or text messages their families use in a month, but they’ll have to keep a close eye on data consumption. Verizon will allow subscribers to adjust their data allowance from month to month, but if they go over their monthly allotment, that will cost $15 per gigabyte.

The data allowances start at $50 per month for one gigabyte. That’s enough for a prudent couple with two smartphones who use Wi-Fi a lot, but Verizon recommends getting two gigabytes for $60. After that, each additional two gigabytes cost an extra $10 per month.

Under “Share Everything,” Verizon will stop charging extra for letting devices act as “mobile Wi-Fi hotspots.” That means subscribers who have a recent smartphone could use it to connect a tablet to the Internet, without paying the extra $10 per month for a tablet.

Moffett sees the new plan as cementing the dominance of Verizon and the No. 2 carrier, AT&T. That’s because the shared-data plan encourages a family to use devices from one company, rather than spreading out the bills.

“In a household with two or three AT&T or Verizon devices – say, a smartphone and a tablet or two, and one device from T-Mobile or Sprint … Sprint doesn’t stand a chance,” Moffett said.