This work proposes the Two-headed DragoNet, a Transformer-based model for hierarchical multi-label classification of financial transactions. Our model is based on a stack of Transformers encoder layers that generate contextual embeddings from two short textual descriptors (merchant name and business activity), followed by a Context Fusion layer and two output heads that classify transactions according to a hierarchical two-level taxonomy (macro and micro categories). Finally, our proposed Taxonomy-aware Attention Layer corrects predictions that break categorical hierarchy rules defined in the given taxonomy. Our proposal outperforms classical machine learning methods in experiments of macro-category classification by achieving an F1-score of 93\% on a card dataset and 95% on a current account dataset.