Photoplethysmography (PPG) is the most widely used non-invasive technique for monitoring biosignals and cardiovascular health, with applications in both clinical settings and consumer health through wearable devices. However, most models applied to PPG data are task-specific and lack generalizability. Limited previous works often used single-device datasets, did not explore out-of-domain generalization, or did not release their models, hindering open research. Here, we introduce PaPaGei, the first open foundation model for PPG signals. Pre-trained on more than 57,000 hours of 20 million unlabeled PPG signals using publicly available datasets exclusively, PaPaGei is evaluated against popular time-series foundation models and other benchmarks on 18 diverse tasks spanning cardiovascular health, sleep disorders, pregnancy monitoring, and wellbeing assessment. PaPaGei's architecture incorporates novel representation learning approaches that examine differences in PPG signal morphology across individuals, enabling it to capture rich representations. Across 18 clinically-relevant classification and regression tasks, PaPaGei outperforms baselines in 13, resulting in an average improvement of 6.3\% and 2.9\%, respectively. Notably, it can be used out of the box as both a feature extractor and an encoder for other multimodal models, opening up new opportunities for multimodal health monitoring