Medical time series (MedTS) classification is critical for a wide range of healthcare applications such as Alzheimer's Disease diagnosis. However, its real-world deployment is severely challenged by poor generalizability due to inter- and intra-dataset heterogeneity in MedTS, including variations in channel configurations, time series lengths, and diagnostic tasks. Here, we propose FORMED, a foundation classification model that leverages a pre-trained backbone and tackles these challenges through re-purposing. FORMED integrates the general representation learning enabled by the backbone foundation model and the medical domain knowledge gained on a curated cohort of MedTS datasets. FORMED can adapt seamlessly to unseen MedTS datasets, regardless of the number of channels, sample lengths, or medical tasks. Experimental results show that, without any task-specific adaptation, the repurposed FORMED achieves performance that is competitive with, and often superior to, 11 baseline models trained specifically for each dataset. Furthermore, FORMED can effectively adapt to entirely new, unseen datasets, with lightweight parameter updates, consistently outperforming baselines. Our results highlight FORMED as a versatile and scalable model for a wide range of MedTS classification tasks, positioning it as a strong foundation model for future research in MedTS analysis.