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While unsupervised domain adaptation methods based on deep architectures have achieved remarkable success in many computer vision tasks, they rely on a strong assumption, i.e. labeled source data must be available. In this work we overcome this assumption and we address the problem of transferring knowledge from a source to a target domain when both source and target data have no annotations. Inspired by recent works on deep clustering, our approach leverages information from data gathered from multiple source domains to build a domain-agnostic clustering model which is then refined at inference time when target data become available. Specifically, at training time we propose to optimize a novel information-theoretic loss which, coupled with domain-alignment layers, ensures that our model learns to correctly discover semantic labels while discarding domain-specific features. Importantly, our architecture design ensures that at inference time the resulting source model can be effectively adapted to the target domain without having access to source data, thanks to feature alignment and self-supervision. We evaluate the proposed approach in a variety of settings, considering several domain adaptation benchmarks and we show that our method is able to automatically discover relevant semantic information even in presence of few target samples and yields state-of-the-art results on multiple domain adaptation benchmarks.