Federal officials last night announced a multimillion-dollar agreement with a private development group that is designed to settle Union Station's mammoth financial problems without further need for federal subsidies for the long-deteriorating rail terminal.

Under the accord, the developers will initially pay the federal government $1 million a year in rent, a fee that is expected to rise to several million dollars annually within a few years.

Officials said the amount will be sufficient to pay off all federal debts and costs of overseeing the complex.

The agreement marked a milestone in the monumental structure's tangled history. The terminal, built in 1907, was closed in 1981 as a hazard. At the time, the federal government had spent $117 million on the station, which is now being restored at an additional cost of nearly $140 million in federal and private funds.

Secretary of Transportation Elizabeth Hanford Dole hailed the new agreement as a key step in "restoring Union Station to the transportation hub it once was and making it the commercial center we envision."

"Once the building is rented up," said S. Mark Lindsey, special counsel for the Federal Railroad Administration and a principal negotiator in the agreement, "it will take the project wholly off the federal budget."

Jeff Gordon, a lawyer for the developers, described the group as confident the project will prove "a commercial success."

The agreement was reached with a partnership formed by Equity Associates, an affiliate of LaSalle Partners; Williams Jackson Ewing, and Benjamin Thompson & Associates Inc.

According to Lindsey, the agreement provides for increases in the initial $1 million-a-year rent that are tied to inflation and profits. The rent will be adjusted, he said, to reflect 40 percent of any increase in the consumer price index, starting two years after the terminal building is reopened in 1987 or 1988.

The payments will also be increased, Lindsey said, to guarantee the government a sizable share of profits.

The developers will pay the government 50 percent of all profits remaining after allowing for operating costs, loan payments and a 10 percent return on their investment.

The developers are expected to lease major sections of the station for restaurants, shops, movie theaters and offices.

Officials say they hope to revive the "vibrant" atmosphere the station had during the height of the railroad era.

"It is a good deal for us and, I think, a reasonable deal for them too," Lindsey said. The agreement is set to last for at least 29 years, with five options allowing it to be extended to 99 years.

In addition to the rental payments, the government is expected to receive revenue from other sources, including parking fees at a garage now being completed behind the station.

These fees will be used by the government to pay off a $3.5 million-a-year lease from private railroad companies, along with a $70 million loan from Amtrak for renovation work.

The rent will also be spent by the Union Station Redevelopment Corp., a nonprofit agency, to oversee the restoration.