Under the plans for the regions, an initial £285m in transitional seed funding will be allocated by the government next year to support mayors and local leaders - and reduce reliance on "fragmented bidding pots" in Whitehall, the Treasury said.
The government will also confirm that it will work with mayors to design a new £1.5bn borrowing facility from 2028, which would allow them to access capital needed to support local priorities.
The Treasury said this could be put towards new homes, bringing high streets back to life, or improving transport links.
Healey said: "Mayors and local leaders know what their communities need to grow, which is why we are giving them more money, more power and more capacity to get projects moving, build homes and make the right decisions for their areas."
Areas across the country which are not yet strategic authorities will be able to access a share of the £285m funding to "unlock projects which will contribute to growth in their areas".
The prime minister said: "I'm calling time on local leaders going cap in hand to Westminster. That is no way to run a country."
Claire Ward, chairwoman of the UK Mayors Network and Labour's East Midlands mayor, said that having the "right powers and resources through increased devolution" would help turn "ambitious plans into reality and deliver real, lasting change" for communities.
Lord Sadiq Khan, Labour's mayor of London, said greater ability to invest could "help unlock transformational infrastructure projects" including the West London Orbital route, the extension of the Bakerloo Underground line and Docklands Light Railway, and the development of Stratford International station.
However, Healey's Budget preparations suffered a blow when the Treasury's entrepreneurship adviser, Alex Depledge, announced she was resigning from the role. She will leave on Thursday, the day after the Budget.
Start-ups, she told the Sunday Times, external, were being treated as a "sideshow" and should not be pushed to the "margins of economic policy".
"Keeping scale-ups on the fringes underestimates the contribution of our greatest companies, and we need to support and develop them on British shores at all costs," she said.
Leading up to the Budget, defence has also remained a key talking point. Healey resigned in June from his role as defence secretary in the previous government over the defence investment plan, which he claimed fell "well short" of what was needed to fund the armed forces.
He had called for defence spending to rise to 3% of the country's GDP by 2030, on the way to reaching a Nato target of 3.5% in 2035.
But urging him to commit to setting out plans to spend 3% of GDP on defence, the shadow chancellor said: "We are living in an era of extraordinary threats, and yet the chancellor is dithering over finding the money to pay the country's insurance premium... you cannot have a strong economy without a strong defence".
Responding to Andrew Griffith's comments, Defence Secretary Wes Streeting said the Conservatives were to blame for failing to invest in the military while in office.
Streeting said the prime minister had made it clear that his government was "determined to give our armed forces the investment needed to keep us safe".
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