Mr Gorbachev, who ended the Cold War without bloodshed but failed to prevent the collapse of the Soviet Union, died at the age of 91.
As leader, Mr Gorbachev forged arms reduction deals with the United States and partnerships with other countries to remove the Iron Curtain that had divided Europe since World War II and triggered the reunification of Germany.
The prime minister said the Soviet leader had changed the world for the better.
"He brought openness to a closed society with his policy of glasnost. With perestroika, he began to restructure a political and economic system deeply resistant to any such attempts," he said in a statement on Wednesday.
"Mikhail Gorbachev was a man of warmth, hope, resolve and enormous courage, and in a world that was profoundly divided, he was driven by an instinct for cooperation and unity.
"Ultimately, he lifted a great shadow that lay across humanity."
Mr Albanese honoured Mr Gorbachev's achievements of freeing eastern European nations from Soviet rule as well as bringing an end to the Cold War.
"With President (Ronald) Reagan, he achieved breakthroughs in arms control, including for some nuclear weapons," he said.
"With his death, we have lost one of the true giants of the 20th century."
Treasurer Jim Chalmers paid tribute, calling Mr Gorbachev a pivotal figure at a defining moment.
"When the world saw conflict and stalemate, he saw peace and possibility," Dr Chalmers told reporters in Canberra.
"He was the epitome of courage and vision, and he was a reminder that it takes more courage to end a war than to start one."
Deputy Prime Minister Richard Marles said Mr Gorbachev would be remembered as a key architect of making the world a safer place.
"For those of us who lived through that period, it was a time of enormous anxiety where there was a sense of existential threat across the world," he told ABC radio on Wednesday.
"(Gorbachev's) dialogue with Ronald Reagan really brought an end to that. He will be forever remembered as a key architect and the world is a much safer place as a result."
Opposition Leader Peter Dutton said Mr Gorbachev's life and death highlighted the stark difference in current Russian leadership under President Vladimir Putin.
"Whilst it's slipped from the headlines, we should remind ourselves every day that these attacks (on Ukraine) are still taking place ... and unfortunately the lessons of the '80s have been lost on President Putin," he told ABC News.
"I hope that we can return to a more sensible age (but) that doesn't seem possible at the moment, which is a tragedy."
Former prime minister Paul Keating said Mr Gorbachev's historic move towards a more open, consultative government was crucial.
"The generosity of spirit about him and his genuineness ... he was able to communicate with people, induce trust and get commitments," he told ABC Melbourne radio.
with Reuters
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