The computational analysis to assist radiologists in the interpretation of mammograms usually requires a pre-processing step where the image is converted into a black and white mask to separate breast tissue from the pectoral muscle and the image background. The manual delineation of the breast tissue from the mammogram image is subjective and time-consuming. The 2D Wavelet Transform Modulus Maxima (WTMM) segmentation method, a powerful and versatile multi-scale edge detection approach, is adapted and presented as a novel automated breast tissue segmentation method. The algorithm computes the local maxima of the modulus of the continuous Gaussian wavelet transform to produce candidate edge detection lines called maxima chains. These maxima chains from multiple wavelet scales are optimally sorted to produce a breast tissue segmentation mask. The mammographic mask is quantitatively compared to a manual delineation using the Dice-Sorenson Coefficient (DSC). The adaptation of the 2D WTMM segmentation method produces a median DSC of 0.9763 on 1042 mediolateral oblique (MLO) 2D Full Field Digital mammographic views from 82 patients obtained from the MaineHealth Biobank (Scarborough, Maine, USA). Our proposed approach is evaluated against OpenBreast, an open-source automated analysis software in MATLAB, through comparing each approach's masks to the manual delineations. OpenBreast produces a lower median DSC of 0.9710. To determine statistical significance, the analysis is restricted to 82 mammograms (one randomly chosen per patient), which yields DSC medians of 0.9756 for the WTMM approach vs. 0.9698 for OpenBreast (p-value = 0.0067 using a paired Wilcoxon Rank Sum test). Thus, the 2D WTMM segmentation method can reliably delineate the pectoral muscle and produce an accurate segmentation of whole breast tissue in mammograms.