Mr Primakov died in Moscow after a prolonged illness, Russian news agency Interfax reported.
Kremlin spokesman Dmitry Peskov said President Vladimir Putin had been informed of the former prime minister's death and was "deeply saddened".
Mr Primakov was head of the Russian government for just eight months between September 1998 and May 1999.
Born in the Ukrainian capital of Kiev in 1929, he was brought up in Tbilisi, the capital of Georgia.
He studied Arabic at the Moscow Institute for Oriental Studies and went on to be a correspondent for state radio and television.
After moving into politics and a stint as the chairman of the Soviet parliament between 1989 and 1990, Mr Primakov played a prominent role in negotiations with Saddam Hussein ahead of the first Gulf War.
When the Soviet Union collapsed in 1991, he was appointed head of Russia's Foreign Intelligence Service (SVR) and later foreign minister in January 1996.
Then in 1998 he was appointed prime minister by then-president Boris Yeltsin, and was credited with introducing difficult reforms and a degree of stability to a country still reeling from financial crisis.
In March 1999, Mr Primakov attempted to prevent Nato strikes against Yugoslavia.
He famously ordered his pilot to turn around midway across the Atlantic while en route to the United States on an official visit, after learning that Washington had decided to launch the air raids. The incident became known as "Primakov's loop".
But Mr Primakov's stint as prime minister was short lived. He was sacked in 1999 by President Boris Yeltsin, who reportedly became fearful of his rising popularity.
Mr Primakov signalled his intention to run in the 2000 presidential election, but dropped out when Kremlin powerbrokers united around Vladimir Putin.
In 2003, he once again travelled to Iraq and met Saddam Hussein in an attempt to prevent war, this time at Mr Putin's request. But three days later a US-led offensive began.
In later life, Mr Primakov headed a business lobby group and was respected as one of Russia's leading elder statesmen.

The Tigers, who sit third in the Premiership behind Saracens and Exeter, suffered a shock loss to struggling Newcastle on Friday.
"The team that played at the weekend was good enough [to win]," Cockerill told BBC Radio Leicester.
"We know that the players we put on Friday can perform better."
Their next opponents Harlequins are only a point behind them despite having won two fewer games.
Cockerill says Leicester have gone back to basics in training as they look to pick up their first league win in the three weeks.
"We revisited some of those fundamentals this week in training," he said. "We have to work hard, get our mindset and attitude right.
"In sport sometimes you don't play as well as you would like to and in a scientific world, sport is not an exact science."

McManus is getting married on Saturday to Dunloy and Antrim camogie player Aileen Martin.
The Cushendall man played a pivotal role as he struck 1-13 in last weekend's dramatic 3-20 to 2-22 extra-time win over Carlow.
Paul Sheehan hit 0-15 for Down as they beat Roscommon 2-24 to 1-20.
However, Down's recent form suggest that the Saffrons should still be good enough to see off the Mourne County with something to spare despite McManus' absence.
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Yevgeny Primakov, a former Russian prime minister, foreign minister and spy chief, has died at the age of 85.
[NEXT_CONCEPT]
Leicester Tigers director of rugby Richard Cockerill has said his side are "far from a crisis point" but need to get their "mindset and attitude right".
[NEXT_CONCEPT]
Antrim will hope Neil McManus' absence will not unduly hinder them in Saturday's Christy Ring Cup game against Down at Cushendall.