The Edinburgh-born athlete became Britain's most successful Olympian this month when he took his tally of medals to six golds and one silver.
Lord Provost Donald Wilson said it was the most prestigious honour the city could bestow.
The council also has plans to honour the city's other London 2012 competitors with a parade.
Only five other people have been given the freedom of the city: the Queen, the Duke of Edinburgh, Sir Sean Connery, Nelson Mandela and Burmese democracy campaigner Aung San Suu Kyi.
The council is also considering plans to celebrate other Olympian and Paralympians with connections to Edinburgh.