MOSCOW, OCT. 2 -- Ida Nudel, whose 16-year struggle to join her family in Israel led to exile in Siberia, said today she finally has been given permission to leave the Soviet Union.

Nudel, whose plight became a cause celebre in the West, said she was informed this afternoon that her application for an exit visa -- repeatedly denied year after year -- would be granted in the coming days.

"I was so excited that at first I can't believe it," Nudel, 56, said in a telephone interview after she returned from Yom Kippur services at a Moscow synagogue.

The Jewish dissident leader, once dubbed "the guardian angel of refuseniks" by other Jews who had been refused permission to leave the Soviet Union, said she would go to Israel as soon as possible to join her sister, Elana Friedman, in Rehoveth. Friedman, who applied to leave in 1971, the same time as her sister, was granted a visa and has been living in Israel with her children during Nudel's long battle with Soviet authorities.

"It takes about three weeks to prepare all the documents," Nudel said, explaining that she does not yet have an exit visa.

She said she immediately went to the home of a friend with a telephone and called physicist Andrei Sakharov, a longtime comrade in Soviet dissident circles. She next telephoned her sister.

Word spread quickly through the community and around the world, Nudel said, and she was inundated with greetings and best wishes.

In a trend that some observers link to Soviet leader Mikhail Gorbachev's policy of improved relations with the West, more than 5,000 Jews have been granted exit visas this year, compared with fewer than 1,000 in 1986.

In 1978, after demonstrating outside the Kremlin and hanging a banner from her window that said "KGB let me go to Israel," Nudel was arrested and sentenced to four years in internal exile in the Siberian town of Krivosheino on charges of "malicious hooliganism."

After her release in 1982, she moved to Bendery, a small town in the southwestern region of Moldavia, but she traveled often to Moscow, staying with friends because she was not permitted to live in the capital.

In New York, Jerry Strober, a spokesman for the National Conference on Soviet Jewry, said Nudel had gone to Moscow for a hearing on her case when she was summoned to a meeting with visa officials who gave her the news.

Morris Abram, chairman of the conference, said, "We heartily welcome the news of Ida Nudel's permission on the eve of our most sacred day, Yom Kippur."

The conference estimates that 380,000 Soviet Jews have asked to leave the country and that 11,000 have had their applications rejected at least once.