The 298ft high-rise flats in Whitevale Street and Bluevale Street, Dennistoun, are the latest to go on the demolition list.
They will join the knockdown queue behind the Red Road flats and the Ibrox high rise flats.
The 29-storey properties in Dennistoun, which have a total of 348 flats, are coming down because people no longer want to live in them and maintenance and running costs are high.
For more than four decades the two towers – which will come down in the next two years – have dominated the East End skyline. Work began in 1967 and was completed the following year.
Apart from the Barbican Estate in London, they are the tallest public housing project ever built in the United Kingdom.
The towers are owned by Glasgow Housing Association, which is upgrading homes across the city and is flattening many of the 1960s blocks.
The tenants are slowly being moved to newly-built properties and other upgraded GHA homes in the areas of their choice or into houses belonging to other Registered Social Landlords.
In nearby Gallowgate, work is expected to begin next month on 62 new homes.
Gallowgate is on the city's Transformational Regeneration Areas, a partnership including the Scottish Government, Glasgow City Council, GHA and other social landlords.
The Areas were set up to help the regeneration of Glasgow through the building of hundreds more homes.
A mix of two and three bedroom homes will be built by Cruden in Gallowgate.
And six ground-floor cottage flats specially adapted for wheelchair users will also be on the new site.
Andy Ashcroft , GHA east area director, said: "The Gallowgate is in line for a massive transformation over the next couple of years.
"We have worked very closely with the community to determine what type of homes the residents want to see.
"Our decision to demolish these two blocks is part of our plans to regenerate communities across Glasgow."
Stephen Birrell, chair of Dennistoun Community Council, said: "I would say the blocks should be demolished.
"We would hope for further investment in quality housing and that development planning, linked to wider regeneration, provides opportunities to improve local infrastructure, including green space, amenity space and public realm.
"Members and partners of Dennistoun Community Council are committed to involving residents and would be keen to contribute to consultation events and initiatives linked to this development."