Council tax will be harmonised across the two areas
Cheshire's political map has changed after 120 years of administration by the county council.
It has been replaced by two unitary authorities - Cheshire West and Chester and Cheshire East.
Three district councils, Ellesmere Port and Neston, Vale Royal and Chester City have been merged to form Cheshire West and Chester.
Congleton, Crewe and Nantwich and Macclesfield make up Cheshire East. Both authorities are Conservative-led.
At Cheshire West and Chester, 230 staff have taken voluntary redundancy as a result of the changes, and 138 in the Cheshire East area.
Council tax is also being harmonised. Those living in Vale Royal will see a rise of 3% and Crewe and Nantwich 1.1%. A rise of just under 1% will affect those in Ellesmere Port and Neston.
Congleton residents' council tax will fall by 1% and in Macclesfield it is unchanged.
On Wednesday, new councillors and a 12-piece band will be on board an open top bus in Cheshire West and Chester.
It will leave Chester for Boughton, Winsford, Northwich and Ellesmere Port.
Councillor Mike Jones, council leader, said: "This is not simply the handover of responsibilities, our new council will think and act differently.
"The projects that we inherit will be continued with added vigour and new projects will be introduced to tackle issues facing our communities and to give the people of this borough a better life."
Councillor Wesley Fitzgerald will lead the new Cheshire East authority, which he says will be a "can-do" council.
"Progressively during the first year, we will settle our service bases across East Cheshire and make our information centres accessible to all," he said.
"We will avoid the town hall/head office syndrome as a key part of our intention to be community-facing."
Cheshire East has been using a mobile information trailer with a directory of councillors and information for residents about how the council will operate.
A special service of thanksgiving and commemoration was held at Chester Cathedral on Sunday to mark the end of Cheshire County Council.