This paper presents a wearable sensor patch with real-time respiration monitoring by measuring the change in thoracic impedance resulting from breathing. A bioimpedance (BioZ) sensor with two sensing electrodes is employed to measure the chest impedance. In addition, a medical-grade infrared temperature sensor is utilized to detect body temperature. The recorded data is transmitted via a Bluetooth module to a computer for online data computation and waveform visualization. The breath-by-breath breathing rate is calculated using the time difference between two BioZ signal peaks, and the results are validated against a commercial respiration monitoring belt. Experimental tests have been conducted on five subjects in both static (i.e., sitting, supine, sleeping on the left side, sleeping on the right side, and standing) and dynamic (i.e., walking) conditions. The experiment measurements show that the BioZ sensor patch can be used to monitor the breathing rate accurately in static conditions with a low mean absolute error (MAE) of 0.71 breath-per-minute (bpm) and can detect breathing rate effectively in a dynamic environment as well. The results suggest the feasibility of using the proposed approach for respiration monitoring in daily life.