The invention provides a sensor for measuring both impedance and ECG waveforms that is configured to be worn around a patient' s neck. The sensor features 1) an ECG system that includes an analog ECG circuit, in electrical contact with at least two ECG electrodes, that generates an analog ECG waveform; and 2) an impedance system that includes an analog impedance circuit, in electrical contact with at least two (and typically four) impedance electrodes, that generates an analog impedance waveform. Also included in the neck-worn system are a digital processing system featuring a microprocessor, and an analog-to-digital converter. During a measurement, the digital processing system receives and processes the analog ECG and impedance waveforms to measure physiological information from the patient. Finally, a cable that drapes around the patient' s neck connects the ECG system, impedance system, and digital processing system.