GENEVA. Switzerland--Secretary of State George P. Shultz announced yesterday night that an agreement has been reached with the Soviet Union to begin negotiations on nuclear missiles and space weapons.

Shultz told a news conference after two days of talks with Soviet Foreign Minister Andrei A. Gromyko that the date and place of the negotiations will be decided through diplomatic channels within one month.

He said he and Gromyko agreed that the talks should ultimately lead to "the complete elimination of nuclear arms everywhere."

A joint statement released before the news conference said. "The sides agree that the subject of the negotiations will be a complex of questions concerning space and nuclear arms, both strategic and intermediate range, with all the questions considered and resolved in their inter relationship."

It said the "objective of the negotiations will be to work out effective agreements aimed at preventing an arms race in space and terminating it on Earth, at limiting and reducing nuclear arms, and at strengthening strategic stability."

In Moscow, the official Soviet news agency Tass carried a dispatch on the Shultz Gromyko statement in its English language service.

The statement said the bilateral "negotiations will be conducted by a delegation from each side divided into three groups."

Shultz told the news conference one group would address space arms, whether based or targeted on Earth or in space while the two other groups would deal with "limitations and reductions in strategic and intermediate range nuclear arms."

Previously, the United Stated and the Soviet Union held two separate negotiations on medium-range and long-range missiles, but the Soviet walked out of those talks in Geneva in late 1983.

Shultz and Gromyko ended two days of talks yesterday. The joint statement was released at 11 p.m., and Shultz then held his news conference in the huge salon of the Intercontinental Hotel.

The two diplomats met for 7 hours and 42 minutes yesterday to try to resume superpower negotiations on arms reductions after a lapse of 13 months.

Resting on the outcome of the talks were the course of armscontrol negotiations as well as the pattern of U.S. Soviet relations in President Reagan's second term.

Shultz and Gromyko arranged their two-day conference to discuss negotiations on the whole range of present nuclear weapons and those which one day could be considered for outer space.

There have been no major arms talks between the superpowers since the Soviets abandoned strategic--long-range--missile talks in Geneva on Dec. 8. 1983. On Nov. 23 of that year they walked out of medium range missile talks when the North Atlantic Alliance began deploying cruise and Pershing 2 missiles in Western Europe.

The Soviets came into the Geneva talks stressing the importance of averting an arms race in space. Mikhall S. Gorbachev, a top-ranking Kremlin leader, said during a London visit in December there was "no real hope" of overall nuclear arms control if the space issue was not first resolved.

But when the 75-year-old Gromyko arrived in Geneva on Sunday for his meetings with Shultz he made no such linkage.

Gromkyo's arrival statement was conciliatory and pledged a "responsible and constructive approach" toward the talks. He said, without going into detail, that he favoured "radical reductions of nuclear arms."

Shulter too, was forthcoming in his arrival statement, saying he had come here "on a mission for peace," and he promised a "constructive and positive attitude" toward tha talks.

On outer space "defensive" weapons, the United States is determined to move ahead with "Star Wars" research under President Reagan's strategic Defense Initiative, claiming the Soviet Union has advanced in a similar field.

Gromyko and Shultz were expected to leave for their capitals this morning. Reagan has scheduled a news conference in Washington tonight