An innovative electrocardiogram compression algorithm is presented in this paper. The proposed method is based on matrix completion, a new paradigm in signal processing that seeks to recover a low-rank matrix based on a small number of observations. The low-rank matrix is obtained via normalization of electrocardiogram records. Using matrix completion, the ECG data matrix is recovered from a few number of entries, thereby yielding high compression ratios comparable to those obtained by existing compression techniques. The proposed scheme offers a low-complexity encoder, good tolerance to quantization noise, and good quality reconstruction.