The Federal Communications Commission yesterday approved a fundamental change in the nationwide telephone billing system that will mean a big increase in local telephone rates and lower long-distance costs beginning a year from now.

The commission's unanimous decision was prompted by the January, 1984, breakup of American Telephone & Telegraph Co. and the rapid emergence of competitive long-distance services.

The average $10 monthly access charge for local residential service will rise by $2 in 1984, regardless of the number of long-distance calls placed. The total additional access charge will come to about $8.50 by 1991 based on today's value of the dollar. State regulatory action is likely to produce further local rate increases.

Long-distance charges are expected to be 30 to 35 percent below today's levels at the end of the seven years, discounting inflation.

Under the current billing system, run by AT&T for the past 40 years, local telephone service was subsidized in part by long distance tolls. The purpose was to provide affordable telephone service for as many people as possible.

But that system was upset by two developments.

On Jan. 8 of this year, AT&T and the Justice Department settled the government's long antitrust suit with an agreement requiring divestiture of the company's 22 local operating companies by Jan. 1, 1984. Seven new regional telephone companies will take their place.

Long before then, AT&T's long-distance business began facing competition from companies such as Washington-based MCI Communications Corp. and Southern Pacific Co.'s Sprint service, offering significantly cheaper long-distance service.

The divestiture means that about $10.5 billion in fixed and operating costs, previously borne by AT&T through its long-distance collections, will become the responsibility of the seven regional companies.

The bulk of the costs being transferred to the locals, $8.5 billion, is fixed -- not related to the number of call made. If these costs are passed directly to local telephone users, their bills would increase by a nationwide average of $7 per month.

Opponents of that kind of pass-through, including House Energy and Commerce Committee Chairman John D. Dingell (D-Mich.) and Rep. Timothy E. Wirth (D-Colo.), chairman of the House telecommunications subcommittee, said such an approach would make telephone access too expensive for lower-income people, violating the principle of universal service.

But supporters of the customer-pay approach said it was the only way to prevent big business long-distance users from deserting the AT&T network in droves for the cheaper competitors. That would force even higher charges for residential users.

The FCC's action yesterday was a compromise:

* The seven-year plan is broken into separate five- and two-year segments.

* Residential customers in the first year would pay a flat rate increase of $2, business customers a flat rate increase of $4, with the remainder to be made up by customer usage fees levied by state regulatory agencies and increased equipment prices charged by telephone companies.

* Residential and business customers will have assumed the full $7 overhead cost by the end of the five-year period, through a combination of direct monthly charges and fees based on the amount of telephone usage.

* But the FCC's goal is to go to a flat rate system of monthly charges, eliminating usage fees. The agency, monitoring the transition process, will decide at the end of the five years whether to proceed to a straight pass-through, which would require both business and residential customers to pay the $7 monthly overhead charge.

Assuming that there has been no major customer defection from the traditional telephone network, the agency, in the remaining two years, will implement the flat rate system, which it describes as the most direct way of recouping overhead costs.

* In the first four years, AT&T will pay a "premium access charge," $1.4 billion in the first year and decreasing by 25 percent in each of the following three years. The access charge is a kind of a handicap placed on AT&T until competing long-distance companies enjoy equal access to the traditional long-distance network.

* At the end of the seven-year transition period, AT&T long-distance customers would be paying about 30 percent to 35 percent less, according to Albert Halprin, chief of the FCC's common carriers bureau. The reason is that the company's long-distance costs would have declined in proportion to the shift to local cost support over the transition period, Halprin said.