Buckingham Palace announced the 96-year-old's death at 3.30am Sydney time.
Mr Albanese said the death had brought sadness to not only the UK and Australia but around the world.
"Amidst our grief, the people of Australia offer our gratitude for a remarkable life lived in service of faith and duty," he said.
"In the coming weeks, we will commemorate our late Queen with every state honour.
"I hope all Australians who wish to pay their respects can participate in the gatherings, commemorations and tributes that will be held, as well as share their own reflections and memories."
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.
Opposition Leader Peter Dutton said the world had never before seen a more "dutiful leader" or "decent human".
"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."
John Howard said he would look back on his meetings with the Queen during his years in power with great affection.
"She had what seemed to me to be a deep curiosity about Australia. She understood different features of Australian life," he said.
Scott Morrison was the last Australian leader to meet with the Queen.
"It was the greatest privilege of my life to meet with her on several occasions," he said.
"She loved the resilience of Aussies and quite in awe of it, particularly rural communities and understood droughts and challenges of farmers."
Kevin Rudd said republicans and monarchists alike had an "enormous affection" and respect for the Queen, while Paul Keating said she was an exemplar of public leadership.
"Her exceptionally long, dedicated reign is unlikely to be repeated; not only in Britain but in the world generally," Mr Keating said.
21°C