The most widely used global land cover and climate classifications are based on vegetation characteristics and/or climatic conditions derived from observational data. However, these classification schemes do not directly stem from the characteristic interaction between the local climate and the biotic environment. In this work, we model the dynamic interplay between vegetation and local climate in order to delineate ecoregions that share a coherent response to hydro-climate variability. Our novel framework is based on a multitask learning approach that discovers the spatial relationships among different locations by learning a low-dimensional representation of predictive structures. This low-dimensional representation is combined with a clustering algorithm that yields a classification of biomes with coherent behaviour. Experimental results using global observation-based datasets indicate that, without the need to prescribe any land cover information, the identified regions of coherent climate-vegetation interactions agree well with the expectations derived from traditional global land cover maps. The resulting global "hydro-climatic biomes" can be used to analyse the anomalous behaviour of specific ecosystems in response to climate extremes and to benchmark climate-vegetation interactions in Earth system models.