Communities and Local Government secretary Eric Pickles has given final approval for the project, which stirred up local controversy about spending priorities amid council cuts to public services.
Under the proposals set out by Shepherd Developments, the original grade II-listed red brick building, which dates back to 1933, will be fully restored.
But a 1980s extension will be demolished to make way for 40,000 sq ft of modern offices.
Work is now expected to get underway in August.
Matt Colledge, leader of Trafford council, said: “This decision means it is now ‘all systems go’ for the much needed refurbishment of the town hall.
“The project is going to save our taxpayers millions of pounds over the coming years and we have been working hard internally to ensure we can begin as soon as possible.”
Last year the Conservative-run council came under fire from Labour councillors for spending money on the project, while facing £60m of cuts.
But the Conservatives maintain the scheme will save £5m over 25 years by avoiding a patch-up approach to maintaining the building.