Glaucomatous optic neuropathy (GON) is a prevalent ocular disease that can lead to irreversible vision loss if not detected early and treated. The traditional diagnostic approach for GON involves a set of ophthalmic examinations, which are time-consuming and require a visit to an ophthalmologist. Recent deep learning models for automating GON detection from digital fundus images (DFI) have shown promise but often suffer from limited generalizability across different ethnicities, disease groups and examination settings. To address these limitations, we introduce GONet, a robust deep learning model developed using seven independent datasets, including over 119,000 DFIs with gold-standard annotations and from patients of diverse geographic backgrounds. GONet consists of a DINOv2 pre-trained self-supervised vision transformers fine-tuned using a multisource domain strategy. GONet demonstrated high out-of-distribution generalizability, with an AUC of 0.85-0.99 in target domains. GONet performance was similar or superior to state-of-the-art works and was significantly superior to the cup-to-disc ratio, by up to 21.6%. GONet is available at [URL provided on publication]. We also contribute a new dataset consisting of 768 DFI with GON labels as open access.