Compressive sensing (CS) is quite appealing as a low-complexity method for the compression of ECG data in resource-limited wearable devices. We propose a codec architecture comprising adaptive quantization and asymmetric numeral systems (ANS) based entropy coding of compressive measurements that can boost the compression ratio without sacrificing reconstruction performance. The quantized Gaussian entropy model for the compressive measurements is estimated directly from the data and is adapted dynamically to achieve better compression. We have tested our encoder with Block Sparse Bayesian learning as well as CS-NET sparse recovery algorithms on the MIT-BIH Arrhythmia database. Our encoder can achieve 5-25\% of additional space savings over compressive sensing. The software code implementing this codec and all scripts for the experimental studies conducted in this work have been released as opensource software on GitHub.