This paper is concerned with a development of a segmentation technique for electrocardiogram (ECG) signals. Such segmentation is aimed at a lossy signal compression in which each segment can be captured by a simple geometric construct such as, e.g., a linear or quadratic function. The crux of the proposed construct lies in the determination of the optimal segments of data over which they exhibit the highest possible monotonicity (or lowest variability) of the ECG signal. In this sense, the proposed approach generalizes a fundamental and commonly encountered problem of function (data) linearization. The segments are genetically developed using a standard technique of genetic algorithms (GAs). The two fundamental GA constructs, namely a topology of a chromosome and a fitness function governing the optimization process are discussed in detail. The chromosome being coded as a series of floating point numbers contains the endpoints of the segments (segmentation points). The fitness function to be maximized quantifies a level of monotonicity of the ECG data encountered within the segments and takes into consideration differences between the extreme values (minimum and maximum) of its derivatives. As a result of the genetic optimization, we build segments of ECG signals encompassing monotonic (increasing or decreasing) regions of the signal exhibiting a minimal level of variability. A series of experiments dealing with several classes of ECG signals (namely, normal, left bundle branch block beat, and right bundle branch block beat) visualize the effectiveness of the approach and shows the specificity of the linear segments of data. Furthermore, we elaborate on the relationship between the values of the fitness function and the approximation capabilities (quantified by a sum of squared errors between the local model and the data) of the segments of the signal and show that these two descriptors are highly related.