Ontology Alignment is an important research problem that finds application in various fields such as data integration, data transfer, data preparation etc. State-of-the-art (SOTA) architectures in Ontology Alignment typically use naive domain-dependent approaches with handcrafted rules and manually assigned values, making them unscalable and inefficient. Deep Learning approaches for ontology alignment use domain-specific architectures that are not only in-extensible to other datasets and domains, but also typically perform worse than rule-based approaches due to various limitations including over-fitting of models, sparsity of datasets etc. In this work, we propose VeeAlign, a Deep Learning based model that uses a dual-attention mechanism to compute the contextualized representation of a concept in order to learn alignments. By doing so, not only does our approach exploit both syntactic and semantic structure of ontologies, it is also, by design, flexible and scalable to different domains with minimal effort. We validate our approach on various datasets from different domains and in multilingual settings, and show its superior performance over SOTA methods.