Scottish Power said the controlled explosion would take place on Saturday 26 September.
The twin chimney stacks are both 149m tall and were constructed in time for the coal-fired power station opening in 1967.
The station generated more than 150 Terawatt Hours (TWh) of electricity in its lifetime but closed two years ago.
The demolition will be overseen by ScottishPower's main contractor, Brown and Mason, who have undertaken similar projects in recent years at the Inverkip and Methil power stations.
The "button press" on the day of the event, which will initiate the demolition of both chimneys, will be carried out by the winner of a charity raffle that is being organised by Longniddry and District Rotary Club.
The controlled explosion is expected to draw large crowds, but an exclusion zone will be put in place to ensure public safety.
ScottishPower said advice about the best public vantage points will be issued in the weeks ahead of the demolition.
East Lothian Council leader Willie Innes said: "The demolition of the Cockenzie chimneys carries mixed emotions for many local residents who have lived and worked in their shadows and consider the structures as a landmark within their community.
"However, the demolition will also signify a new start for the area and the council is encouraged by interest shown in new economic opportunities for the site."
A date has been set for the demolition of the landmark Cockenzie Power Station chimney stacks in East Lothian.