The Dorset Street flat complex is set for a €65 million regeneration that will see 158 new housing units being built.
The existing 113 apartments, which were built in the 1960s, will be demolished as part of the revamp.
The current units have been found to have poor energy efficiency with sub-standard kitchens and bathrooms.
There is also a poor site layout that officials say has facilitated anti-social behaviour.
The Department of Housing has given Stage 1 approval for the new development, which will be constructed in three phases.
Phase 1 will see the demolition of the existing St Mary’s Place block and the construction of eight apartments and 11 houses.
Phase 2 will include the demolition of the second and third blocks at St Mary’s Place and Dorset Street to facilitate the construction of 96 apartments.
The final existing block will be demolished as part of Phase 3.
A creche building and the construction of the remaining 43 units will be built as part of the final phase.
Dublin City Council is considering providing the third phase as affordable or cost rental apartments.
Current tenants of the complex will be moved out as part of the plan, with 47 already being vacated.
The council plan to re-house the tenants Dominick Street and North King Street complexes which are currently under construction.
