Biological brain age predicted using machine learning models based on high‐resolution imaging data has been suggested as a potential biomarker for neurological and cerebrovascular diseases. In this work, we aimed to develop deep learning models to predict the biological brain age using structural magnetic resonance imaging and angiography datasets from a large database of 2074 adults (21–81 years). Since different imaging modalities can provide complementary information, combining them might allow to identify more complex aging patterns, with angiography data, for instance, showing vascular aging effects complementary to the atrophic brain tissue changes seen in T1‐weighted MRI sequences. We used saliency maps to investigate the contribution of cortical, subcortical, and arterial structures to the prediction. Our results show that combining T1‐weighted and angiography MR data led to a significantly improved brain age prediction accuracy, with a mean absolute error of 3.85 years comparing the predicted and chronological age. The most predictive brain regions included the lateral sulcus, the fourth ventricle, and the amygdala, while the brain arteries contributing the most to the prediction included the basilar artery, the middle cerebral artery M2 segments, and the left posterior cerebral artery. Our study proposes a framework for brain age prediction using multimodal imaging, which gives accurate predictions and allows identifying the most predictive regions for this task, which can serve as a surrogate for the brain regions that are most affected by aging.