Under an £18m deal, the contractor will carry out both internal and external upgrade works to Drake Court, Grenville Court, Nelson Court and Rodney Court in the old town.
The project includes removing existing render cladding to be replaced with terracotta cladding, resolve cold bridging and thermal issues.
Existing balconies will be replaced with “wintergarden” enclosed balconies.
Sprinkler systems will be fitted in all existing flats as part of the Project Admiral plan, which will get underway next year.
Most of the flats in the four blocks are owned by the council but managed on its behalf by Poole Housing Partnership.