Machine learning offers powerful advantages in sensing systems, enabling the creation and adaptation of high-order signal models by exploiting the sensed data. We present a general-purpose processor that employs configurable machine-learning accelerators to analyze physiological signals at low energy levels for a broad range of biomedical applications. Implemented in 130nm LP CMOS, the processor operates from 1.2V-0.55V (logic). It achieves real-time EEG-based seizure detection at 273μW (at 0.85V) and patient-adaptive ECG-based cardiac-arrhythmia detection at 124μW (at 0.75V), yielding overall energy savings of 62.4× and 144.7× thanks to the accelerators.