After several years of mutual recriminations and hostile rhetoric on both sides, the announcement today in Moscow and Washington that new Soviet-American arms control talks are to be started in January was greeted here with considerable optimism.

The announcement by Vladimir Lomeiko, the new chief spokesman for the Foreign Ministry, came after a day of rumors and speculation pointing to the resumption of the arms control process.

Lomeiko seemed to sum up the mood here by commenting on the absence of questions following the announcement that Foreign Minister Andrei Gromyko and Secretary of State George P. Shultz would meet in Geneva on Jan. 7 and 8.

Today's news, Lomeiko said, "speaks for itself."

In his brief encounter with reporters, Lomeiko made several points concerning the meaning of today's announcement.

The talks, he asserted, "are new negotiations" and not a resumption of the previous negotiations on strategic and medium-range weapons that were suspended by Moscow last year after NATO began deployment of U.S. medium-range nuclear missiles in Western Europe.

"These will be absolutely new negotiations," he added for emphasis.

He would not respond to questions about the substance of these new talks beyond saying, as the official statement said, that they would deal with "the entire complex of questions concerning nuclear and space weapons" and that they were undertaken with a bilateral agreement that the aim was to achieve "mutually acceptable accords."

By stressing the "absolutely new negotiations," Lomeiko sidestepped the matter of previous Soviet insistence that the United States agree to remove the new Pershing II and cruise missiles deployed in Western Europe before any resumption of the talks the Soviets had suspended.

Diplomats suggested, however, that Moscow appeared to have backed down from this stance, a shift that seemed to indicate a political success for President Reagan despite the fact that the Soviets have deployed their own new missiles in Eastern Europe, added more nuclear missile carrying submarines to their forces patrolling waters around the United States and started deploying long-range cruise missiles on Soviet submarines and strategic aircraft.

In their talks in Geneva, Lomeiko said, Gromyko and Shultz will decide on the subject of the future negotiations and their objectives.

Today's announcement came just over a year after first U.S. medium-range missiles arrived in Europe.

On its face, the formulation of the announcement today suggests a compromise between Moscow's interest in starting negotiations on banning militarization of outer space and Washington's insistence on talking about strategic missiles.

It also suggests that the Soviets have accepted Reagan's formula for an "umbrella" approach to the problem.

Georgi Arbatov, the Kremlin's adviser on U.S. affairs, suggested to reporters today that the Soviet Union was prepared to take "a broad approach and not to pick out one issue or two."

Arbatov, speaking after a meeting with British Labor Party leader Neil Kinnock, also reflected optimism in Moscow when he said, "I hope something will happen" in the forthcoming negotiations. He said he thought a return to more normal Soviet-American relations was possible "if there is a political will in Washington," but cautioned that this was "going to take time."

Lomeiko, Arbatov and other Soviet officials insisted that it was the "principled position" of Moscow as announced by President Konstantin Chernenko on several occasions that made it possible to begin "absolutely new negotiations" on arms control.

In retrospect, it seems apparent that Chernenko has been more flexible than his predecessor, Yuri Andropov, who set the removal of U.S. missiles from Europe as a condition for resuming negotiations in a statement last Nov. 24, one day after the Soviets walked out of the Geneva medium-range nuclear weapons talks.

It is expected that Moscow will revive this requirement in a different form in the course of the talks. But this would come in the future, diplomats here said, although they suggested that the problem could be solved eventually by a straight trade-off system.

There is little doubt that the resumption of dialogue would lead to an improved East-West climate.

One indication of this was the arrival yesterday of American singer John Denver, who will have a series of concerts here as a guest of the Soviet government. It is the first such visit in nearly four years.