Automated detection and segmentation of nuclei from high-resolution histopathological images is a challenging problem owing to the size and complexity of digitized histopathologic images. In the context of breast cancer, the modified Bloom-Richardson Grading system is highly correlated with the morphological and topological nuclear features are highly correlated with Modified Bloom-Richardson grading. Therefore, to develop a computer-aided prognosis system, automated detection and segmentation of nuclei are critical prerequisite steps. We present a method for automated detection and segmentation of breast cancer nuclei named a convolutional neural network initialized active contour model with adaptive ellipse fitting (CoNNACaeF). The CoNNACaeF model is able to detect and segment nuclei simultaneously, which consist of three different modules: convolutional neural network (CNN) for accurate nuclei detection, (2) region-based active contour (RAC) model for subsequent nuclear segmentation based on the initial CNN-based detection of nuclear patches, and (3) adaptive ellipse fitting for overlapping solution of clumped nuclear regions. The performance of the CoNNACaeF model is evaluated on three different breast histological data sets, comprising a total of 257 H&E-stained images. The model is shown to have improved detection accuracy of F-measure 80.18%, 85.71%, and 80.36% and average area under precision-recall curves (AveP) 77%, 82%, and 74% on a total of 3 million nuclei from 204 whole slide images from three different datasets. Additionally, CoNNACaeF yielded an F-measure at 74.01% and 85.36%, respectively, for two different breast cancer datasets. The CoNNACaeF model also outperformed the three other state-of-the-art nuclear detection and segmentation approaches, which are blue ratio initialized local region active contour, iterative radial voting initialized local region active contour, and maximally stable extremal region initialized local region active contour models.