Sir Keir spoke of being 'bold about pushing power and resource out of Whitehall' and said that 'those with skin in the game know what's best for their communities'.
The PM said he would be meeting with Mr Burnham - and all other Metro mayors - on Tuesday.
And he vowed his door would always be open to regional leaders 'regardless of the colour of their rosette' who 'want to deliver for their area', adding: "There's no monopoly on good ideas."
The news will be welcomed by Mr Burnham, who has clashed with the Conservative government over Covid, the cancelled HS2 rail line and train services.
Speaking at a Downing Street press conference yesterday, his first as Prime Minister, Sir Keir said he would be setting off today to 'be in all four nations' to meet with first ministers. He said he would be going to Scotland first, then Northern Ireland and Wales before heading back to England.
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