Communities secretary Sajid Javid announced the areas will have control over an investment fund of £600m over the next 30 years.
They will also elect a mayor on 4 May.
“The people of Cambridgeshire and Peterborough came up with an ambitious devolution deal which puts them in charge of decisions that matter to them,” Javid said, announcing the deal in Wisbech yesterday.
“This multi-million pound investment into the region is proof that we’re backing Cambridgeshire and Peterborough with the resources they need.”
The region will also have powers over housing and planning, and transport and skills – with particular responsibility for the adult education budget.
The East of England area will receive £100m from the Housing Investment Fund and an additional £70m ring-fenced for Cambridge city to meet its housing needs
“With powers over transport, skills and housing all coming to the area, I’d urge residents to head to the polls on 4 May and vote for their new mayor,” Javid said.