It's official: Nancy Reagan and Raisa Gorbachev will get together in Geneva when President Reagan and Soviet leader Mikhail Gorbachev hold their first summit meeting there in November.

"There's been an exchange of letters between the two ladies and details are being worked out," Elaine Crispen, Mrs. Reagan's press secretary, said yesterday, confirming reports on CBS News earlier this week. "It could take the form of a tea or a reciprocal tea."

James Rosebush, the first lady's chief of staff, said that Mrs. Reagan is "very pleased" about Raisa Gorbachev's reply to her letter expressing the hope that they might spend some time together.

Rosebush, who met with Soviet officials in Geneva last week, said Mrs. Reagan's schedule in Geneva is still being worked out but that he is "very confident" a meeting between the two women will take place.

Whatever event American and Soviet officials eventually agree upon as appropriate, the setting is likely to provide the two first ladies an informal way in which to get acquainted that might not be possible at official joint functions they attend with their husbands.

Mrs. Reagan initiated the exchange of letters after deciding that she wanted to tell Raisa Gorbachev of the expectations Americans have for a successful summit. In that context, she told aides, she also wanted Gorbachev to know that she was looking forward to meeting her. "It was a case of why not be right up front about it and let Mrs. Gorbachev know?' " said a White House source.

Since nothing that involves the Soviet Union, not even a tea party, is being treated casually by the Reagan administration in its presummit preparations, Mrs. Reagan's idea of writing directly to Mrs. Gorbachev had to be run past President Reagan's foreign policy advisers.

"The National Security Council and State Department heartily concurred in Mrs. Reagan's desire to communicate with Mrs. Gorbachev," Rosebush said.

From then on the typewritten letter, signed by Nancy Reagan, took the diplomatic route to Moscow. Secretary of State George Shultz handed it to Soviet Ambassador Anatoliy Dobrynin, who saw to it that it reached the Kremlin.

When Rosebush and other White House officials making the survey trip to Geneva arrived there, Soviet summit planners already knew about Nancy Reagan's letter. The Americans had Raisa Gorbachev's answer in hand by the time they returned to Washington.

"Basically, it was the same kind of letter as Mrs. Reagan's," said a source, characterizing the exchange as "very open."

Speculation is mounting that the trim, chic Raisa Gorbachev will give Nancy Reagan a run for media attention at the Nov. 19-21 summit, and that on some occasions the two of them might upstage their husbands.

"She seems to be a very attractive person from the standpoint of media consumption," a Reagan administration official said of Raisa Gorbachev.

She and Mrs. Reagan have more in common than fashionable clothes. Like Mrs. Reagan, whose evaluations of people close to President Reagan have a major influence at the White House, Raisa Gorbachev, 51, is described by Soviet and western observers as having insight and offering unvarnished assessments of people and situations.

She has a PhD in philosophy and lectures on Marxism-Leninism at Moscow University. Beyond that and the fact that she and Gorbachev met at Moscow University, have a daughter who is a doctor, and are grandparents, little is released about her by the Soviet government.

She has assumed a public role, however, unparalleled by her predecessors and rare for wives of Soviet officials. Not since Nikita Khrushchev's wife, Nina Petrovna, have westerners been so aware of a Soviet first lady.