He died of a stroke, the agency said, quoting literary sources in Moscow.
Solzhenitsyn served with the Red Army in World War Two but became one of the most prominent dissidents of the Soviet era, enduring labor camps, cancer and persecution by Soviet officialdom.
His experience in the network of labor camps was vividly described in his "One Day in the Life of Ivan Denisovich."
His major works, including "The First Circle" and "Cancer Ward" brought him world admiration and the 1970 Nobel Literature Prize.
Stripped of his citizenship and sent into exile in 1974 after the publication of "The Gulag Archipelago," his monumental history of the Soviet police state, the writer settled in the United States, returning to post-Soviet Russia as a hero in 1994.
He was born on December 11 1918, studied physics and mathematics at Rostov University and became a Soviet army officer after Hitler's invasion in 1941.
Another beacon of my generation, now gone. I have not agreed with everything he had said and done, but he was an amazing writer; I have almost all his Soviet-era books. It is good to know that he has lived a long and full life. Still, he will be missed.