The Nobel laureate had suffered from high blood pressure in recent years.
After returning to Russia, Solzhenitsyn wrote several polemics on Russian history and identity.
He died in his home in the Moscow area, where he had lived with his wife Natalya on Sunday, Stepan told Itar-Tass.
Mrs Solzhenitsyn told Moscow Echo radio her husband lived "a difficult but happy life".
A Day in the Life of Ivan Denisovich was the single book which showed me the power of literature to change the world. Philip Larmett, Kiev, Ukraine
Former Soviet leader Mikhail Gorbachev, whose reforms led to the end of communism in the country, said Solzhenitsyn played a key role in undermining Stalin's totalitarian regime.
His works "changed the consciousness of millions of people", Mr Gorbachev said.
Prisoner, patient, writer
He spent the next eight years in the Soviet prison system, or Gulag, before being internally exiled to Kazakhstan, where he was successfully treated for stomach cancer.
However, within a decade, the writer awarded the 1970 Nobel Prize for Literature was out of favor again for his work, and was being harassed by the KGB secret police.
In 1973, the first of the three volumes of Archipelago, a detailed account of the systematic Soviet abuses from 1918 to 1956 in the vast network of its prison and labour camps, was published in the West.
Its publication sparked a furious backlash in the Soviet press, which denounced him as a traitor.
Early in 1974, the Soviet authorities stripped him of his citizenship and expelled him from the country.
A look at the life of Alexander Solzhenitsyn
He settled in Vermont, in the US, where he completed the other two volumes of Archipelago.
While living there as a recluse, he railed against what he saw as the moral corruption of the West.
Scathing of Boris Yeltsin's brand of democracy, he did not return to Russia immediately upon the collapse of the USSR in 1992, unlike other exiles.
His homecoming in 1994 was a dramatic affair as he travelled in slowly by land from the Russian Far East.
Years later he was embraced by then-Russian President Vladimir Putin, who presented him with Russia's State Prize.
There was significant irony in the fierce critic of Soviet repression being hailed by a former senior officer of the KGB, says the BBC's James Rodgers in Moscow.
Mr Putin described Solzhenitsyn's death as a "heavy loss for Russia".
Solzhenitsyn's latter works, which included essays on Russia's future, stirred controversy.
In 2000, his last major work Two Hundred Years Together examined the position of Jews in Russian society and their role in the Revolution.