Regular screening for the early detection of common chronic diseases might benefit from the use of deep-learning approaches, particularly in resource-poor or remote settings. Here we show that deep-learning models can be used to identify chronic kidney disease and type 2 diabetes solely from fundus images or in combination with clinical metadata (age, sex, height, weight, body-mass index and blood pressure) with areas under the receiver operating characteristic curve of 0.85–0.93. The models were trained and validated with a total of 115,344 retinal fundus photographs from 57,672 patients and can also be used to predict estimated glomerulal filtration rates and blood-glucose levels, with mean absolute errors of 11.1–13.4 ml min⁻¹ per 1.73 m² and 0.65–1.1 mmol l⁻¹, and to stratify patients according to disease-progression risk. We evaluated the generalizability of the models for the identification of chronic kidney disease and type 2 diabetes with population-based external validation cohorts and via a prospective study with fundus images captured with smartphones, and assessed the feasibility of predicting disease progression in a longitudinal cohort.