Heart-related ailments have become a significant cause of death around the globe nowadays. Due to lifestyle changes, people of almost all age brackets face these issues. Preventing and treating heart-related issues require electrocardiogram (ECG) monitoring of the patients. The study of patients' ECG signals helps doctors identify abnormal heart rhythm patterns by which screening problems like arrhythmia (irregular heart rhythm), myocardial infarction (heart attacks), and myocarditis (heart inflammation) are possible. The need for 24-hour heart rate monitoring leads to the development of wearable devices, and constant monitoring of ECG data leads to generating a large amount of data since wearable systems are resource-constrained regarding energy, memory, size, and computing capabilities. The optimization of biomedical monitoring systems is required to increase their efficiency. This project presents an ECG compression system to reduce the amount of data generated which reduces the energy consumption due to the transceiver, which is a significant part of the overall energy consumed. The proposed system uses hybrid Golomb-Rice coding for data compression which is a lossless data compression technique, the data compression is performed on the MIT BIH arrhythmia database, and the achieved compression ratio of the compression system is 2.89 and 3.6 for average and maximum values which when compared to the raw ECG samples requires less transmission cost in terms of power consumed.