He takes the reins at the think tank and lobbying body on 1 September, replacing Anna Feuchtwang who quit to join charity Everychild as chief executive at the beginning of July.
Edwards will report to CEO Martin Pilgrim and will be responsible for 16 staff, covering public affairs, internal and external comms and publications.
Acting director of comms and public affairs Steve Pearce will return to his head of corporate communications post when Edwards joins the association.
The ALG lobbies on local government issues in London and provides transport services and housing advice to the capital’s residents. It distributes £27m a year in grants to voluntary groups.
Edwards joins the ALG after three years in his Westminster-based post, where he was responsible for all political output for BBC Wales.
Prior to BBC Wales, he edited the Local Government Association’s weekly magazine First, a title produced for all councillors in England.
Edwards also previously held posts at a number of charities, including Children in Need and human rights campaigner Liberty.
He said: ‘For the last three years, I have been reporting on the agenda, but now I will be setting the agenda.’
He added: ‘The biggest challenges will be highlighting what London councils achieve and to gain greater resources and power for London councils.’