Planned extensive upgrade works include fire safety work, kitchen and bathroom replacement and mechanical and electrical works.
Southwark estimates the upgrade work will be worth up to £835m over a 10-year term.
It has broken the upgrade plan into the four contract areas:
1. Borough and Bankside/Walworth – £215m
2. Rotherhithe/Bermondsey – £206m
3. Camberwell/Peckham – £208m
4. Nunhead and Peckham Rye/Dulwich – £205m
Shortlisted firms will be invited to submit tender in April.
Further details can be obtained by emailing Southwark Council.