His spokeswoman Marina Davitashvili said he died after a long illness.
Mr Shevardnadze swept across the international stage in the final years of the Soviet empire, helping topple the Berlin Wall and end the Cold War.
However, as the leader of post-Soviet Georgia his career in the public eye ended in humiliation. He was chased out of parliament and forced into retirement amid claims of a rigged parliamentary election.
As Soviet foreign minister, he was the diplomatic face of Mikhail Gorbachev's liberalising policies of glasnost and perestroika, or transparency and reform.
He impressed Western leaders with his charisma, quick wit and commitment to Mr Gorbachev's course of reforms.
He helped push through the withdrawal of Soviet troops from Afghanistan in 1989, signed landmark arms control agreements and helped negotiate German reunification in 1990 - a development Soviet leaders long feared and opposed.
Western leaders would remain grateful for Mr Shevardnadze's work as foreign minister.
Mr Shevardnadze returned to Georgia and after becoming the country's leader in 1992 survived two assassination attempts.