Electrocardiogram (ECG) signals are the biomedical signals commonly used in the prognosis of cardiovascular diseases. ECG recordings need to be stored and transferred when telemedicine-based healthcare systems are required. These data are stored in a digitized format at higher bits per sample that requires ample space for storage. Therefore, this motivated us to develop efficient compression methodologies for ECG signals. In this regard, this work proposes compression techniques using the optimized tunable-Q wavelet transform (TQWT). For this purpose, TQWT parameters are optimized using several meta-heuristic optimization algorithms such as variants of PSO, ABC and its hybrid with PSO, GWO and its hybrid with PSO, and Sparse PSO. These hybrid methods and Sparse PSO have been utilized for the first time to optimize TQWT. Subsequently, thresholding and quantization are performed by using a dead-zone quantizer (DZQ). The quantized coefficients are encoded by utilizing a lossless compression technique run-length encoding (RLE). The proposed algorithms have been examined on the MIT-BIH arrhythmia database. It is clear from the results that significant compression has been achieved when compared to existing techniques. The performance of the proposed algorithms has been evaluated in terms of various evaluation parameters that are compression ratio (CR), percent-root-mean square difference (PRD), signal-to-noise ratio (SNR), and quality score (QS).