The late monarch was a unifying force throughout her 70-year reign, the prime minister said in an address at an Australia House Commemorative Luncheon in London on Saturday (AEST).
"Even as history continued to shape us, and the bond between our two nations evolved, the affection and respect in which we held Her Majesty remained – unchanged, undiminished," he said.
"The Queen transcended barriers. You could be a republican, and still feel nothing but regard for her."
During a visit to Australia in 2000, months after Australia held a republic referendum, the Queen expressed her deep connection to the nation.
The revered monarch said she "felt part of this rugged, honest, creative land" and has "shared in the joys and the sorrows, the challenges and the changes that have shaped this country's history".
Mr Albanese recalled the Queen's 16 visits to Australia, including a day at the races with former prime minister Bob Hawke in 1988, which he described as "one of the most Australian experiences of all".
He also hailed the monarch's loyalty and unwavering commitment to royal life.
"She celebrated our good times, and stood with us in our times of trial, bringing sympathy and comfort when it was so badly needed," the prime minister said.
Soon after touching down, Mr Albanese and his partner Jodie Haydon laid a small bouquet of white flowers at Green Park in Westminster.
"It's a great honour to be representing Australia here," he said.
"Quite clearly, what we can see all around us is the affection in which Her Majesty Queen Elizabeth was held by people here in the United Kingdom but also of course in Australia and right around the Commonwealth."
Mr Albanese, Ms Haydon and Governor-General David Hurley later signed the official book of condolence at Lancaster House in London.
The prime minister - along with other world leaders - met King Charles III later in the day, cementing Australia's importance to the new monarch.
Mr Albanese also met with new British prime minister Liz Truss.
Downing Street framed the conversation as a chat rather than formal bilateral talks.
The two leaders shared condolences, and reflected on continuing close connections at all levels between Australia and UK.
Mr Albanese said the Queen's funeral would be a "sombre day".
"But it will also be a day of celebrating a life well lived, a life of service," he said.
The monarch's funeral will be televised at 8pm (AEST) on Monday.
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