West German police said that Shcharansky, 38, was handed over to U.S. Ambassador Richard Burt at the Glienicke Bridge.
In Tel Aviv, Israel Radio said Prime Minister Shimon Peres asked South African President Pieter W. Botha to free Nelson Mandela as part of the exchange.
Botha had suggested 10 days ago in a speech to Parliament that he might agree to such a step if Shcharansky and another Soviet dissident, Andrei Sakharov, as well as a South African soldier held prisoner in Angola, were freed.
Israel Radio reported Mandela might be freed as early as Wednesday. There was no official confirmation from Israeli officials, and no immediate comment from South Africa's white-led government.
Shcharanksy waved to a crowd of bystanders and well-wishers, as Burt's Mercedes-Benz roared past a crowd of waiting journalists and drove to West Berlin's Templehof Airport. There, the former computer programmer was put aboard an executive jet that flew to Frankfurt where he was reunited with his wife, Avital. They had not seen each other for eight years. Frankfurt airport officials said they took off for Israel aboard a special flight provided by the Israeli government. The two planned to live in the Jewish state.
Shcharansky, one of the most prominent dissidents in the Soviet Union, was sentenced in 1978 to 13 years after being convicted of spying for the CIA - a charge he repeatedly denied.
Shcharansky, a Jew, said his only crime was applying for permission to emigrate to Israel.
In Washington, the White House issued a statement confirming Shcharansky's release and describing him as "a prisoner of conscience." It said the release was a "the product of close U.S.-German cooperation over an extended period of time.
"The president has expressed his warm appreciation to Chancellor (Helmut) Kohl," the White House said.
The spy swap started behind a screen of buses across the center of the Glienicke Bridge shortly before 11 a.m. (4 a.m. CST). The bridge has been the site of numerous past exchanges, including that of U-2 spy plane pilot Gary Powers for Soviet master spy Rudolf Abel on Feb. 10, 1962.
Shcharansky's car pulled off the bridge - connecting the Potsdam area of East Germany with the American sector of West Berlin - more than 30 minutes ahead of the remaining East bloc prisoners.
Crowds of officials could be seen on the center of the bridge, but the U.S. military buses obscured what was taking place behind.
Traveling in the opposite direction across the bridge linking the American sector of West Berlin to the Potsdam section of East Germany were the Koecher couple and three others jailed on spy charges in West Germany.
As a condition for his exchange, Koecher, 52 pleaded guilty to espionage eight days ago and was sentenced to life in prison. The pleading occurred at a closed hearing in U.S. District Court in Manhattan, according to an attorney for the couple, Steven Westby of Atlanta.
Federal prosecutors believed that they would have had a difficult time convicting Koecher because of the way CIA and FBI agents handled the couple's 1984 arrest, according to Justice Department and FBI sources.
The CIA agent on the case, according to court records, told the couple they could leave the United States if they revealed what they knew. But the FBI later decided to use Koecher's admissions as a basis for prosecuting them. The earlier statements made by the CIA agent and the circumstances of the arrests cast doubt on whether anything the couple said during their 12-day interrogation could be used against them at trial.
Koecher and his wife, Hana, came to the United States 20 years ago as Czech defectors. Actually, he had been trained for two years in Czechoslovakia as an intelligence officer and "successfully penetrated" the CIA, according to a court complaint filed by the FBI.
For 2 1/2 years - from February 1973 to August 1975 - Koecher worked as a translator and consultant for the CIA, passing "virtually any" classified materials he was able to obtain, the complaint said. After working for the CIA from 1973 to 1977, Koecher taught humanities from September 1979 to August 1980 at the Old Westbury campus of the State University of New York.
According to the FBI, Koecher is believed to have caused the death of a Soviet official who was really a U.S. mole. The official, Aleksander Ogorodnik, who worked in the Soviet Ministry of Affairs, died in 1977 during an interrogation by the KGB, the FBI said.
The FBI said that while Koecher worked for the CIA, Hana Koecher was his courier, carrying the secret information to Czech intelligence agents in Europe. But she was not charged with any crime.
Instead, she was held as a material witness to appear before a grand jury. However, she refused to answer any questions, asserting a wife's privilege not to testify against her husband.
In addition to the Koechers, the following Soviet bloc agents were sent home in today's exchange:
Jerzy Kaczmarek, 33, an officer in the Polish secret service, held in West Germany since his arrest in March 1985 in connection with spying in the Bremen area.
Yevgeni Semliakov, 39, a Soviet computer specialist who worked at his country's trade mission in Cologne, West Germany, was sentenced in September 1985 to three years in prison for trying to obtain high technology that is banned for export to the Soviet bloc.
Detlef Scharfenort, East German intelligence man, serving a four-year prison sentence in West Germany since last June for recruiting students to spy for his country.
In addition to Shcharansky, the East bloc released to the West:
Wolf George Frohn, 41, an East German sentenced in his country to life imprisonment in 1981 after being convicted of spying for the CIA.
Jaroslav Jaworski, a Czechoslovak sentenced in 1981 to 12 years in prison for helping East Germans flee to the West.
Dietrich Nistroy, 50, a West German sentenced in East Germany in 1982 to life imprisonment on a conviction of spying for West Germany's intelligence service.