The pair met for just over half an hour in Bali on Tuesday afternoon, a significant moment for the relationship between the two nations.
In opening remarks ahead of the meeting, Mr Albanese told Mr Xi the Australia-China relationship was an important one.
"We need to work towards a stable, prosperous and peaceful Indo-Pacific and an international system that is governed by international law," he said.
"We have had our differences and Australia won't resile from our interests or our values.
"But our bilateral relationship is an important one. Both sides have worked to stabilise the relationship based on mutual respect and mutual benefit."
Malcolm Turnbull was the last Australian prime minister to have a formal meeting with Mr Xi in 2016.
Since then, increasing tensions over security arrangements and trade sanctions worth $20 billion have seen relations deteriorate.
But Mr Albanese, who set no preconditions for the formal talk, considered securing the meeting a success in itself.
Indonesian President Joko Widodo is keen for the two-day summit to deliver outcomes, as the world grapples with rising inflation, climate change and the effects of the pandemic.
He called for unity and said collaboration was "badly needed" to save the world.
Ahead of the meeting, Treasurer Jim Chalmers said while it was a welcome opportunity, it would not immediately fix the fractured relationship between the two countries or result in the removal of trade sanctions.
"I don't think anybody pretends that some of the issues China has raised, certainly some of the issues that we have raised, will be solved overnight," he told ABC radio.
"We give ourselves a much better chance where there's engagement and dialogue, and there will be today."
Dr Chalmers said the government remained deeply concerned over the detention of two Australians, including journalist Cheng Lei, who has been in custody for more than two years and denied contact with her family.
Liberal Senator Simon Birmingham welcomed the end of the Chinese government's ban on talks with Australia but urged Mr Albanese to protect Australia's interests.
"It was always counterproductive for China to refuse to sit down at the table with Australia," he told reporters in Sydney.
"Dialogue should be the last thing ended rather than the first thing."
The head of Australia's peak business group, in Bali for a meeting of industry groups, described the meeting as a "tremendous reset" with China.
"We've obviously had a set of difficulties in the relationship but you can't fix those if you don't have a dialogue," Business Council of Australia chief Jennifer Westacott said on Monday.
"This creates an opportunity for businesses to come in behind that reset the prime minister has done and start building relationships."
Mr Albanese has also confirmed bilateral talks with British Prime Minister Rishi Sunak, French President Emmanuel Macron and Indian Prime Minister Narendra Modi.
Russia's invasion of Ukraine provides a backdrop to the summit, as Foreign Minister Sergei Lavrov attends instead of President Vladimir Putin.
Ukrainian President Volodymyr Zelenskiy addressed the summit virtually.
Leaders at the G20 summit have taken part in two closed sessions on health, food and energy security.
with Associated Press