Describing the space‐time variability of hydrologic extremes in relation to climate is important for scientific and operational purposes. Many studies demonstrated the role of large‐scale modes of climate variability such as the El Niño-Southern Oscillation (ENSO) or the North Atlantic Oscillation (NAO), among many others. Climate indices have hence frequently been used as predictors in probabilistic models describing hydrologic extremes. However, standard climate indices such as ENSO/NAO are poor predictors in some regions. Consequently, this paper describes an innovative method to avoid relying on standard climate indices, based on the following idea: the relevant climate indices are effectively unknown (they are hidden), and they should therefore be estimated directly from hydrologic data. In statistical terms, this corresponds to a Bayesian hierarchical model describing extreme occurrences, with hidden climate indices treated as latent variables. This approach is illustrated using three case studies. A synthetic case study first shows that identifying hidden climate indices from occurrence data alone is feasible. A second case study using flood occurrences at 42 east Australian sites confirms that the model correctly identifies their ENSO‐related climate driver. The third case study is based on 207 sites in France, where standard climate indices poorly predict flood occurrence. The hidden climate indices model yields a reliable description of flood occurrences, in particular their clustering in space and their large interannual variability. Moreover, some hidden climate indices are linked with specific patterns in atmospheric variables, making them interpretable in terms of climate variability and opening the way for predictive applications.