Despite the communicative importance of negation, its detection remains challenging. Previous approaches perform poorly in out-of-domain scenarios, and progress outside of English has been slow due to a lack of resources and robust models. To address this gap, we present D-Neg: a syntax-aware graph reasoning model based on a transformer that incorporates syntactic embeddings by attention-gating. D-Neg uses graph attention to represent syntactic structures, emulating the effectiveness of rule-based dependency approaches for negation detection. We train D-Neg using 7 English resources and their translations into 10 languages, all aligned at the annotation level. We conduct an evaluation of all these datasets in in-domain and out-of-domain settings. Our work represents a significant advance in negation detection, enabling more effective cross-lingual research.