The internationally renowned architects will act as lead designer and consultant for the redevelopment of the Grade-II listed Old Royal London Hospital in Whitechapel.
The council approved plans for the creation of a new town hall at the site last November.
Further features of the scheme include refurbishing John Onslow House in Roman Road, which AHMM will also act as lead design consultants.
The Civic Centre project is part of the council's wider Whitechapel regeneration, which includes Crossrail opening in 2018.
The 10-year regeneration also includes 3,500 new homes, 5,000 jobs, new retail opportunities and new public spaces.
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As part of the winning tender, AHMM has agreed to provide a range of wider community benefits including providing access to jobs and work experience for local residents.
Pupils also interested in a career in design and architecture will be mentored, while the practice will work closely alongside schools on curriculum projects.
Will Tuckley, Chief Executive at Tower Hamlets Council said: "I am pleased to announce that the experienced AHMM team have been appointed to lead the architectural design and consultation stage of our ambitious plans to create a new Civic Centre in the heart of Whitechapel.
"Whitechapel as a whole is undergoing massive changes and the Civic Centre will be a key building contributing to the regeneration of the area and securing the future of a building of heritage importance for the borough.
"I know that they will relish the particular challenges that the building will bring and look forward to working with the team to deliver a truly fantastic new civic and public service hub for the borough and our residents."
Paul Monaghan, Director of AHMM, added: "This is an amazing opportunity to create a civic beacon for Tower Hamlets, and we look forward to the challenge of working with new and old to make a new type of town hall at the heart of the community."
The contract covers all consultant, design and planning management milestones including the appointment of contractors and work taking place on site.
The new building is due to be completed by the end of 2021.
(LM)
