Lyubimov died peacefully in his sleep on Sunday morning, three days after he went into hospital, his wife Katalin informed, reported the New York Times.
Besides his wife, survivors include a son, Peter, and several grandchildren.
Lyubimov founded the Taganka Theatre in 1964. He staged adaptations of John Reed's '10 Days That Shook the World' about the Bolshevik Revolution and dozens of works of literature that did not obviously lend themselves to a theatrical treatment.
He also staged plays that were implicitly, and sometimes not so implicitly, critical of the Soviet system.
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The theatre became more popular after actor Vladimir Vysotsky, whose politically charged ballads had earned him a devoted following, joined the troupe.
Lyubimov was stripped of his citizenship, his apartment was seized and he was removed from his post at the Taganka after he went to London to stage a version of 'Crime and Punishment' and openly criticised the Soviet leadership in newspaper interviews.
He spent five years in exile, navigating the globe as a theatre and opera director, to much acclaim. He was invited back to Moscow in 1988 to help stage a production of 'Boris Godunov'. The next year he was officially welcomed home, given his citizenship back and restored to his post at the Taganka.
He, however, continued to direct elsewhere, and his adaptation of the Dostoyevsky novel 'The Possessed' was presented as part of a celebration of his 95th birthday.