"I said we'd take power out of Westminster and carry it into every postcode in the country. Today, we make good on that promise," Burnham added.
"Soon, every local leader will have the power and resources to improve public transport, build homes and create jobs."
Treasury officials stated that detailed operational mechanics and equalisation formulas will be announced alongside Chancellor John Healey's autumn budget.
The equalisation system aims to prevent wealthier regions like London from pulling away from areas with slower economic growth.
"The people who best understand what skills employers want, what transport an area needs and where investment can make the biggest difference are those who live there," said John Healey, Chancellor of the Exchequer.
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"For the first time we're giving Mayors a share of income tax so communities directly benefit when their economy grows."
Cabinet ministers noted that areas without an elected mayor will form strategic authorities to ensure non-mayoral regions retain access to devolved funding streams.
"This is the first step in our plan to rewire this country and build a better future, where power is no longer hoarded in Westminster but is put back in the hands of local people," said Angela Rayner, Secretary of State for Housing, Communities and Local Government.
First Secretary of State Louise Haigh defended the regional distribution model during media appearances. She confirmed that central formulas will balance revenue differences across regions.
"There is already a way that the business rates retention is distributed to correspond with central funding formula to correct for that," Haigh said.