The towers will be brought down by a controlled explosion at noon on Saturday 26 September.
A second controlled explosion soon after will demolish the turbine hall at the East Lothian power station.
An exclusion zone will be in place from 09:00 to ensure that the demolition can be carried out safely.
The safety restrictions will cover the Greenhills, sections of Edinburgh Road and the John Muir Way, as well as extending in to the Firth of Forth.
Traffic restrictions will also be in place around the power station from 07:00.
Scottish Power said viewing locations in the immediate vicinity of the power station would be very limited.
Police Scotland and East Lothian Council recommended people who would like to watch the demolition take the time to plan their position in advance.
Insp Andy Harborow said: "The iconic Cockenzie chimneys have been standing tall within the local community for almost fifty years and we anticipate many members of the public will turn out for their demolition.
"To preserve the safety of those in attendance, we have been working alongside our partners at East Lothian Council and Scottish Power to identify and create a suitable exclusion zone for the demolition.
"No vantage points or parking spaces have been allocated to view this event and so anyone visiting the area is asked to be considerate to the local community and try to minimise any disruption."
The twin chimney stacks are both 149m tall and were constructed in time for the coal station opening in 1967.
The turbine hall structure is predominantly made of steel.
The "button press" to initiate the demolition of both chimneys, will be carried out by East Lothian resident Donald McCulloch, the winner of a charity raffle.
Details have been released of the demolition of the landmark twin chimney stacks at the former Cockenzie Power Station site.