NEW YORK — T-Mobile USA, the struggling No. 4 cellphone company, is ditching plans centered on familiar two-year contracts in favor of selling phones on installment plans.

T-Mobile is the first major U.S. carrier to break from the contract model. The company changed its website over the weekend to begin selling the new plans. It plans to lay out the rationale for the change on Tuesday at an event in New York.

T-Mobile has been losing subscribers from its contract-based plans for more than two years, chiefly to bigger competitors Verizon Wireless and AT&T. T-Mobile has done better with contract-less, prepaid plans, but those aren’t as profitable for the company.

The new plan blurs the boundaries between the two types. Prepaid plans have lower monthly fees, but the buyer usually has to pay full or nearly full price for the phones. With T-Mobile’s new plans, the initial phone-buying experience won’t be much different from what it’s like for contract plans, but customers could save money in the long run.

For instance, someone who wants a Samsung Galaxy S III would pay $70 upfront and then $90 per month for unlimited calling, text and data. That monthly fee includes $20 to pay off the cost of the phone over two years.

By separating the cost of the phone from the service, T-Mobile is making its plans and upgrade options easier to understand. When the phone is paid off, the $20 fee in that example disappears. On traditional contract-based plans, the buyer is deemed to have “paid off” the phone after a certain period of time and become eligible for a new, subsidized phone, but the monthly payments don’t decline.

As before, T-Mobile’s prices generally undercut those of the bigger phone companies. The chief downside is that its data network coverage is poorer in rural areas.

T-Mobile stopped short of adopting shared-data plans that Verizon Wireless and AT&T introduced last year. Those plans allow all of a family’s devices to share a pool of monthly data usage. Instead, T-Mobile is selling data per line in three tiers. The talk and text portion of the plan comes with 500 megabytes of data usage per month. Adding $10 bumps that to 2 gigabytes per month, while adding $20 provides unlimited data.

A big part of the reason for the exodus of contract-signing customers from T-Mobile is that it, alone among the four national-level cellphone carriers, doesn’t offer the iPhone. That’s because its network has, until recently, not been able to offer high-speed data service to iPhones. It’s now able to offer high-speed data to iPhones in some cities, and had been trying to persuade iPhone owners who have come off their contracts with AT&T to move the phones over to T-Mobile.

T-Mobile is a unit of Germany’s Deutsche Telekom AG, which has agreed to merge it with No. 5 carrier MetroPCS Communications Inc. That deal faces opposition from shareholders of MetroPCS, which provides only prepaid service.