The governing body of the IAG is its Council, consisting of the officers (President, Vice President, Immediate Past President, Honorary Secretary and Honorary Treasurer) and up to six members. Council may co-opt up to eight additional members to fulfil specific roles. For example, the Chair of the organising committee of the next Geoanalysis conference is usually co-opted to Council.
Council is elected every three years by ballot of the membership, with the results being announced at the General Meeting held during the Geoanalysis conference. Nominations for membership of Council are sought three or four months before the conference.
Council meets usually twice a year hosted by one of its members. Meetings last typically two to three days depending on the agenda and if there is, for example, a special workshop scheduled, involving outside experts.
| Jacinta Enzweiler | President | University of Campinas, Brazil |
| Regina Mertz-Kraus | Vice-President | Johannes Gutenberg-Universität, Mainz, Germany |
| Jennifer Cook | Secretary | British Geological Survey Nottingham, UK |
| Chris Jackson | Treasurer | Kent, UK |
| Thomas Meisel | Immediate Past President | Montanuniversität Leoben, Austria |
| Peter Webb | GeoPT Programme | The Open University, Milton Keynes, UK |
| Stephen Wilson | G-Probe Programme | United States Geological Survey, Denver, USA |
| Doug Miles | IAGeo Limited | Nottingham, UK |
| Dieter Garbe-Schönberg | Member of Council | University of Kiel, Germany |
| Charles Gowing | Member of Council | British Geological Survey Nottingham, UK |
| Mike Pribil | Member of Council | US Geological Survey, Denver, USA |
| Axel Renno | Member of Council | Helmholtz Centre Dresden-Rossendorf, Germany |
| Martin Rosner | Member of Council | Isoanalysis, Berlin, Germany |
| Michael Wiedenbeck | Member of Council | Helmholtz Centre Potsdam, Germany |
| Edward Williams | GGR Business and Publication Manager | Centre de Recherches Pétrographiques et Géochimiques, Nancy, France |