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Chernenko, 73, died yesterday after a long illness - but his death was only announced to the Soviet people this morning. Sombre music preceded the news on radio and television and scheduled programmes were cancelled.
The speed of naming of his successor - at 54 the youngest man to take over as general secretary of the Soviet communist party - has taken people by surprise.
In another break with tradition, Mr Gorbachev has announced arms talks with the Americans in Geneva will go ahead tomorrow.
Chernenko lasted only 13 months in the top job. He was in poor health when he was appointed and his death was caused by heart failure brought on by problems with his lungs and liver.
He is the third Soviet leader to die in just over two years. Leonid Brezhnev died in 1982 after 18 years in power. He was 75. Yuri Andropov died 18 months later aged 69.
The British Prime Minister Margaret Thatcher will attend Chernenko's funeral on Wednesday - but the United States President Ronald Reagan will not be going.
The BBC's Moscow correspondent, Tim Sebastian, says Mr Gorbachev's appointment marks a dramatic change in leadership in Moscow.
He says Mr Gorbachev is a dynamic figure who has moved rapidly through the Soviet hierarchy.
"There seems little doubt the Gorbachev administration will look different. More outgoing, more approachable, more concerned with its public image," he reported.
"But its aims and its approach seem likely to be familiar. Despite his lively and flexible manner, Gorbachev is still a strict, orthodox Marxist in no sense has he shown himself to be a liberal."
Mr Gorbachev's acceptance speech gave a hint of the changes to come. He spoke of his desire to freeze the deployment of weapons and reduce the international nuclear weapons stockpiles.
Mrs Thatcher has already indicated her approval at his appointment. Following his recent visit to Britain, she said: "I like Mr Gorbachev. We can do business together."
Mikhail Gorbachev radically changed the course of Soviet foreign policy, signing a number of agreements with the United States on nuclear disarmament.
He introduced a policy of openness or "glasnost" and he was also the architect of "perestroika" or deep political and economic reforms. But his reforms led to severe economic hardship at home. Growing nationalist movements spearheaded by the Baltic states led him to propose a loose federation of Soviet states.
But this proved the last straw for communist hardliners. In August 1991 he survived a coup attempt - largely thanks to the support of the Russian authorities, under the leadership of Boris Yeltsin.
Yeltsin continued to attract more support which led eventually to the resignation of Gorbachev on 25 December 1991. The Soviet flag, the hammer and sickle, was lowered for the last time on 31 December.
Gorbachev is now president of the Green Cross - an organisation concerned with the clean-up of chemical and biological weapons.
His wife Raisa, the only wife of a Soviet leader to become a public figure in recent times, died of leukaemia in 1999.
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