By 2040, age-related macular degeneration (AMD) will affect ~288 million people worldwide. Identifying individuals at high risk of progression to late AMD, the sight-threatening stage, is critical for clinical actions, including medical interventions and timely monitoring. Although deep learning has shown promise in diagnosing/screening AMD using color fundus photographs, it remains difficult to predict individuals' risks of late AMD accurately. For both tasks, these initial deep learning attempts have remained largely unvalidated in independent cohorts. Here, we demonstrate how deep learning and survival analysis can predict the probability of progression to late AMD using 3298 participants (over 80,000 images) from the Age-Related Eye Disease Studies AREDS and AREDS2, the largest longitudinal clinical trials in AMD. When validated against an independent test data set of 601 participants, our model achieved high prognostic accuracy (5-year -statistic 86.4 (95% confidence interval 86.2-86.6)) that substantially exceeded that of retinal specialists using two existing clinical standards (81.3 (81.1-81.5) and 82.0 (81.8-82.3), respectively). Interestingly, our approach offers additional strengths over the existing clinical standards in AMD prognosis (e.g., risk ascertainment above 50%) and is likely to be highly generalizable, given the breadth of training data from 82 US retinal specialty clinics. Indeed, during external validation through training on AREDS and testing on AREDS2 as an independent cohort, our model retained substantially higher prognostic accuracy than existing clinical standards. These results highlight the potential of deep learning systems to enhance clinical decision-making in AMD patients.