Atmospheric transport inversion is commonly used to infer greenhouse gas (GHG) flux estimates from concentration measurements. The optimal location of ground-based observing stations that supply these measurements can be determined by network design. Here, we use a Lagrangian particle dispersion model (LPDM) in reverse mode together with a Bayesian inverse modelling framework to derive optimal GHG observing networks for Australia. This extends the network design for carbon dioxide (CO2) performed by Ziehn et al. (2014) to also minimise the uncertainty on the flux estimates for methane (CH4) and nitrous oxide (N2O), both individually and in a combined network using multiple objectives. Optimal networks are generated by adding up to five new stations to the base network, which is defined as two existing stations, Cape Grim and Gunn Point, in southern and northern Australia respectively. The individual networks for CO2, CH4 and N2O and the combined observing network show large similarities because the flux uncertainties for each GHG are dominated by regions of biologically productive land. There is little penalty, in terms of flux uncertainty reduction, for the combined network compared to individually designed networks. The location of the stations in the combined network is sensitive to variations in the assumed data uncertainty across locations. A simple assessment of economic costs has been included in our network design approach, considering both establishment and maintenance costs. Our results suggest that, while site logistics change the optimal network, there is only a small impact on the flux uncertainty reductions achieved with increasing network size.