MOSCOW, SEPT. 7 -- Jewish activist Josef Begun received permission to leave the Soviet Union for Israel today, ending a 16-year wait and one of the most bitter personal battles with Kremlin authorities in modern Soviet history.

Nine other prominent Jews were also told that their requests to emigrate were settled, marking a sudden change for the better in the plight of some longstanding Soviet refuseniks, the term given Soviet Jews who have been denied exit visas.

In an interview here tonight, Begun -- who was released in February from Chistopol prison -- called the decision "a miracle." Breaking away from an emotional celebration in his tiny apartment with friends still awaiting permission to emigrate, the 54-year-old Begun said, "I am the happiest man alive."

When the call came from Moscow's visa office at noon today, he said he turned to his wife Inna, who began to cry.

With the resolution of Begun's case and those of such prominent refuseniks as Vladimir Lifshitz and Victor Brailovsky, the status of Soviet refuseniks takes one of its most dramatic turns since late 1979, when the flow of Jews to the West fell sharply, and exit applications and stories of painful waits began to accumulate.

Western diplomats in Moscow interpreted the development as a Soviet attempt to create a positive atmosphere for the meeting between Soviet Foreign Minister Eduard Shevardnadze and Secretary of State George P. Shultz in Washington next week.

The meeting, scheduled from Sept. 15-17, is expected to center on settling details of a U.S.-Soviet arms accord and the dates for a third summit meeting between President Reagan and Kremlin leader Mikhail Gorbachev. "The Soviets seem to be responding to a U.S. plea for some movement in the human rights area, and at the same time to be trying to preclude human rights from becoming a major issue during the talks," one western diplomat said.

Even as he embraced his wife and son, however, Begun criticized Soviet authorities for their treatment of Jews who want to stay as well as those who want to emigrate.

"They resolve a few cases of well-known people to make it look like the situation is changing," he said, "but in reality it is not. I understand this as only a window to show that it is better."

After his initial application to emigrate in 1971, Begun had his requests to leave denied so often and with such vehemence that he became a symbol for all refuseniks. A mathematician by training, Begun lost his job when he applied to leave.

After his first application was rejected, Begun dug in his heels and became a teacher of Hebrew and Jewish culture to those who had no other opportunity to learn them. "My knowledge is far from perfect," said Begun, whose spoken English is better than his Hebrew, "but I teach those who know even less than I do."

Arrests and beatings in the early 1970s at the hands of Soviet intelligence, or KGB, gave way to harsher treatment, as Begun was swept up in a wave of arrests of Jews and jailed for two years for parasitism, a catch-all term for Soviets without official employment. Within months of his 1979 release he was arrested again and sentenced to three years for living in Moscow without permission.

In 1982, Begun was imprisoned again and finally released from Chistopol prison last February in a mass release of over 100 political prisoners, and after week-long demonstrations by his wife, Inna, and son, Boris, at the central Arbat street.

After his release, Begun quickly regained his position as the most beloved and outspoken of Soviet Jewish activists remaining here.

It was a place he had earned through years of commitment to the faith and unremitting criticism of the shortage of rabbis, synagogues and respect for Jewish culture across the Soviet Union.

During his long wait for permission to go, Begun watched many other close friends gain release from prison and permission to emigrate, including Anatoly (now Natan) Shcharansky and Yuri Orlov, human rights activists now in the West.

"I wanted to leave this country of no freedoms," Begun said in explaining his initial decision to emigrate as a 38-year-old struggling for his Jew-ish identity. "I did not feel free here as a person or as a Jew."

Other well-known refuseniks also granted permission to leave included Lev and All Sud, Symeon Yankovsky, and Arkady and Helen Mai and their daughter Naomi.

The list of those contacted by the Soviet emigration office was notable for its inclusion of those who have waited for more than a decade and sometimes up to 15 years to leave. It consisted exclusively of Jews with a commitment to go to Israel, not the United States. The number of Jews waiting to leave is still in the tens of thousands, according to most western estimates.

They include other prominent figures who have waited for years, such as Naum Meiman, a 76-year-old mathematician, who has waited for more than 10 years to go to the United States, and who was with other refuseniks in Begun's kitchen tonight.

For them, too, Begun sought to offer some consolation in his moment of jubilation. "When you wait so long," he said, "you don't quite believe it when it happens. And then you feel joy and sorrow: joy for your new life and sorrow for those being left behind."