Four deals have been signed off in what deputy Prime Minister Angela Rayner described as ‘only the first step' of the Government's devolution drive.
If approved by Parliament, the agreements will allow residents in Lincolnshire and in Hull and east Yorkshire to elect regional mayors.
Combined county authorities will also be established in Devon & Torbay and Lancashire.
Rayner said: ‘This is only the first step of our major ambition to drive forward our devolution revolution, and ensure we empower more communities and strengthen the existing powers of our brilliant mayors.'
The Government also said it was ‘minded' to progress with four non-mayoral devolution agreements with Cornwall Council, Buckinghamshire Council, Warwickshire CC and Surrey CC.
Lincolnshire CC leader Martin Hill said: ‘Having a combined authority will give us the ability to liaise directly with the Government about what is best for our residents and we'll be able to achieve our ambitious plans more quickly.'