The ECG (Electrocardiogram) signal represents electrical activity of heart and is recorded for monitoring and diagnostic purpose. These signals are corrupted by artifacts during acquisition and transmission predominantly by high frequency noise due to power line interference, electrode movements, etc. Addition of these noise change the amplitude and shape of the ECG signal which affect accurate analysis and hence need to be removed for better clinical evaluation. In this paper, ECG signal taken from MIT -BIH database is first denoised using Total Variation Denoising (TVD); using Majorization minimization (MM) optimization technique. ECG signals generate massive volume of digital data, so they need to be suitably compressed for efficient transmission and storage. Hence, for efficient compression the signal is segmented into various sections using Bottom-Up approach. The individual sections are then approximated using Chebyshev polynomials of suitable orders. The performance of the approximation technique is measured by computing the Maximum Absolute Error, the Compression Ratio, Root Mean Square Error, Percent Root Mean Square Difference and Percent Root Mean Square Difference Normalized. The results are also compared with other techniques as reported in the literature, where significant improvements in all the performance metrics are observed.