Mr Albanese's cabinet met in Canberra on Wednesday for the first time after officially being sworn in by Governor-General David Hurley at Government House.
The 30-strong ministry lineup contains the first female Muslim minister in Anne Aly and the first Muslim to serve in cabinet with Ed Husic joining the frontbench in the industry and science role.
Linda Burney becomes the first woman, and the second First Nations person, to serve as Indigenous affairs minister and will take the lead on enshrining a voice to parliament in Australia's constitution.
"I am proud of my experienced, diverse and energised team," Mr Albanese said on his Facebook page after the ceremony.
"We are ready to deliver on a better future for all Australians, and we'll start with focusing on how we can help families deal with rising costs."
Ms Burney wore a kangaroo-skin cloak made by Lynette Riley, her Wiradjuri sister who sang her into parliament when she was elected.
It featured her personal totem, the white cockatoo, which is a messenger in Wiradjuri culture.
Speaking after the ceremony, Treasurer Jim Chalmers said a priority would be talks with Energy Minister Chris Bowen and Resources Minister Madeleine King on power prices.
"These challenges will not be addressed overnight but it's important we work hard together to address them," Dr Chalmers told reporters.
The treasurer has already spoken with his state and territory counterparts, regulators, peak business groups and unions as he works on an economic statement to be delivered in July, an employment summit and white paper, and an October budget.
"The situation we have inherited is serious and in some instances dire," he said.
"And we can only deal with these economic challenges if we work together - state, federal, local government, business, employers, employees," he said.
The major cabinet shakeup by Mr Albanese had some questioning the shift of more senior MPs, after Tanya Plibersek was withdrawn from the education and women portfolios and moved to environment and water.
NSW MP Jason Clare was given the education portfolio while Finance Minister Katy Gallagher has responsibilities for women.
Deputy Labor leader Richard Marles defended the shift for Ms Plibersek, saying the environment ministry could not be characterised as a demotion, with the area front and centre of Labor's priorities.
"It's one of the most important ministries we have got, which has been an enduring passion for Tanya Plibersek," the new defence minister told the Nine Network.
"It's always been a very senior portfolio in government, particularly Labor governments."
Thirteen women were appointed to a ministerial role with a record 10 in the 23-person cabinet.
Aged Care Minister Anika Wells says she joined parliament after being inspired by women activists.
"The decision for me to run for parliament was made after I gave birth to a baby girl. I was diagnosed with an aggressive chronic disease and hospitalised regularly," she told the ABC.
"During one of those moments I watched the women's marches on TV and thought about how those women were marching because they felt they could not be complacent about their role in the world.
"That was a real lightning-bolt moment for me."
The swearing in coincided with Labor securing 77 seats in the House of Representatives, after the marginal constituency of Gilmore on the NSW south coast was called for incumbent Fiona Phillips.
Labor is expected to have 26 seats in the Senate, relying on 12 Greens senators and one crossbencher to pass legislation if the coalition is not on side.
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