The venue, which was built for the 1970 Commonwealth Games, will be replaced with a new £41m sports centre that is due to open in Easter 2020.
The new centre will be partly funded by residential and commercial development on parts of the existing site.
This will include development of affordable and low cost housing through the Council’s 21st Century Homes Programme.
New sports centre, designed by Holmes Miller
The first multi-sport games hall will be equivalent in size to an eight-court badminton hall with permanent seating for 420 and additional bleacher seating for 725. The second hall is set to be the equivalent of a four-court badminton hall with permanent seating for 430.
Councillor Ian Campbell, Vice Convener of Culture and Communities for the City of Edinburgh Council, said: “This is the end of an era for Meadowbank and the start of a major redevelopment to support physical activity, health and wellbeing in Edinburgh for generations to come.
“The facility will support both the local community and clubs and it is important we get the design right. That is why the facility mix has been revisited, and now incorporates improved indoor athletics facilities in line with feedback from individual users and sports clubs within the budget we have available.”