Eitan, the handler for Jonathan Pollard, a US Navy analyst who passed Israel thousands of top secret documents, was himself wanted by American authorities for a time.
He died in the afternoon at Tel Aviv’s Ichilov hospital, the radio said, without giving further details.
“Rafi was one of the heroes of the state of Israel’s intelligence service in countless acts for Israel’s security,” Prime Minister Benjamin Netanyahu said in a statement.
“We mourn his passing.”
Eitan also won a rare eulogy from the Shin Bet domestic security service, for whom he had worked.
“Rafi, who was one of the founders of the Shin Bet’s operations branch, led and participated in dozens of groundbreaking operations that will remain unknown for many years to come,” agency chief Nadav Argaman wrote in a statement.
“We grieve at his passing and are proud to continue on his path.”
Eitan was born on a kibbutz in British-ruled Palestine in November 1926.
He was nicknamed “Rafi the Stinker” after he fell into a sewer during a military operation prior to the establishment of Israel in 1948.
After his service in the elite Palmach arm of the paramilitary Haganah organisation, the forerunner of the Israeli army, he joined Mossad in the 1950s.
He rose to become the agency’s operations chief, commanding the operation to snatch Eichmann in the Argentinian capital Buenos Aires and smuggle him to Israel.
The mastermind of the Nazis’ Final Solution, Eichmann was then tried and hanged.
The ability of the security services to bring him to justice was a source of pride for the Jewish state, which President Reuvin Rivlin called a momentous moment in Israel’s history.
In the 1980s, Eitan’s name came into the spotlight in a major crisis between Israel and key ally the United States.
He was the handler for Jonathan Pollard, a US marine analyst who handed thousands of top secret documents over to Israel between May 1984 and his arrest in November 1985.
Pollard served 30 years in a US prison. He was freed in November 2015 but given a five-year probation period during which he is barred from travelling.
The FBI had also issued an arrest warrant against Eitan, Pollard’s handler.
In 2006, at the age of 79, he was elected to Israel’s parliament as head of the Pensioners’ Party and appointed minister for senior citizens.
“I had a heart operation a year ago, I can’t see anything and I can’t hear anything, but I run every morning, I sculpt and my wife says I’m doing well,” Eitan said on becoming a lawmaker.
Israeli President Reuven Rivlin said in a statement Saturday evening that Eitan “was a born fighter who stuck to his mission and to what he knew to be right.”
“Our heads are bowed today in his memory,” he said.