Under the plan the two counties would share an elected mayor to oversee transport, highways maintenance, house building and strategic planning.
They would get Â£750m over 30 years for infrastructure and Â£130m for housing.
The government said the cash would go elsewhere if the idea was rejected, and councils have been given two weeks to vote on whether to support the offer.
Four Norfolk councils - Norwich, Great Yarmouth, North Norfolk and Breckland - have already pulled out of discussions.
But the government decided East Anglia devolution should go ahead with the remaining 12 authorities.
"This is one of the most ambitious deals in the country," said Andy Wood, the Suffolk businessman who oversaw the negotiations.
"But the secretary of state is clear that if we don't agree the deal the funding on offer will be spent elsewhere in the country."
Under the plans the mayor would have a cabinet comprising one representative from each council and one from New Anglia Local Enterprise Partnership.
The cabinet will have the power to vote down the mayor's decisions.
Councils have expressed concerns about loss of powers, and critics have questioned if the money on offer really is new.
It is understood the government will announce that if any of the four councils have a change of heart they would be allowed to join at a later date.
But with significant opposition at King's Lynn and West Norfolk Council and Norfolk County Council, the deal could yet be scuppered.
Plans for a mayor in Cambridgeshire have already been agreed.
The government has given the go-ahead to devolution for Norfolk and Suffolk in what it says is a final offer.