Buckingham Palace announced the 96-year-old's death at 3.30am Sydney time.
Mr Albanese said the nation would remember the Queen as a wise and enduring presence.
"Her Majesty celebrated our good times and she stood with us during trials and hardships, happy and glorious," Mr Albanese said in a televised address on Friday morning.
In coming days, Mr Albanese will travel to London with Governor-General David Hurley to express sorrow on behalf of Australians.
The Queen visited Australia 16 times during her reign, travelling to every state and territory.
During her first visit to Australia in February 1954, 70 per cent of Australians turned out to catch a glimpse of the young monarch.
"Throughout her reign Queen Elizabeth II showed her deep affection for our country," Mr Albanese said.
Opposition Leader Peter Dutton said the world had not seen a more "dutiful leader" or "decent human" than the Queen.
"That extraordinary life which touched so many has sadly come to an end," he said.
"The last page has been inked on an exceptional reign ... a monarch who ruled with an absolutely huge heart and wisdom both innate and gained from almost a century of life and experience.
"Her Majesty was gentle, kind and much loved."
Former prime minister Tony Abbott said the Commonwealth had lost an "exemplar of duty, honour and faithfulness".
"Although I served the the Australian people as prime minister, I was always conscious of a duty to her as sovereign," he said.
"It is so typical of this remarkable woman that she was discharging her duty till her last day on this earth."
Scott Morrison, who was the last Australian leader to meet with the Queen, said she had an affinity with Australia.
"It was the greatest privilege of my life to meet with her on several occasions," he told Sydney radio station 2GB.
"She loved the resilience of Aussies and quite in awe of it, particularly rural communities and understood droughts and challenges of farmers.
Former prime minister Kevin Rudd said like many, he was in a state of shock and had expected the Queen to recover as she had with past illnesses.
"I didn't really believe it," he told ABC News.
"In meeting folks like myself, she was also extraordinarily well briefed ... and she's just a person with a great sense of fun and a sense of humour."
Mr Rudd said republicans and monarchists alike had an "enormous affection" and respect for the Queen.
Foreign Minister Penny Wong said she was "deeply saddened" by the death.
"Her Majesty's historic reign was defined by her dignity, strength and her dedication to service," she said.
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