The two agencies pitched jointly for the account against a shortlist of undisclosed agencies.
Moving People, the working title given to a planned long-running campaign from Mental Health Media, Mind, Rethink and the Institute of Psychiatry at King's College London, will run over the next three years.
The aim of the project is to fight stigma and discrimination experienced by people with poor mental health.
The programme's activities will include a national advertising campaign designed to change public attitudes to mental health.
The programme will also include six national and 28 community projects throughout England, which will involve people with mental health problems in a variety of physical activities aimed at improving their mental and physical wellbeing.
The charities were awarded £16 million from the Big Lottery Fund and £2 million from Comic Relief to run the programme. The £18 million total budget is intended to include marketing spend.
Miles Calcraft Briginshaw Duffy was awarded the advertising account for Moving People in June, following a pitch against M&C Saatchi, Euro RSCG and an undisclosed agency.
Moving People is modelled on similar programmes elsewhere in the world, and is part of an international movement sharing best practice.