The CO2CRC Otway Project is Australia's first demonstration of the geological storage of carbon dioxide (CO2), where about 65,000 metric tons of fluid consisting of 92% CO2 and 8% methane (CH4) by mass have been injected underground. As part of the project objective of developing methodologies to detect, locate and quantify potential leakage of the stored fluid into the atmosphere, we formulate an inverse atmospheric model based on a Bayesian probabilistic framework coupled to a state-of-the-art backward Lagrangian particle dispersion model. A Markov chain Monte Carlo method is used for efficiently sampling the posterior probability distribution of the source parameters. Controlled experiments used to test the model involved releases of the injected fluid from one of the nearby wells and were staggered over one month. Atmospheric measurements of CO2 and CH4 concentrations were taken at two stations installed in an upwind-downwind configuration. Modeling both the emission rate and the source location using the concentration measurements from only two stations is difficult, but the fact that the emission rate was constant, which is not an unrealistic scenario for potential geological leakage, allows us to compute both parameters. The modeled source parameters compare reasonably well with the actual values, with the CH4 tracer constraining the source better than CO2, largely as a result of its six times higher signal-to-noise ratio. The results lend confidence in the ability of atmospheric techniques to quantify potential leakage from CO2 storage as well as other source types.