White matter tract segmentation, i.e. identifying tractography fibers (streamline trajectories) belonging to anatomically meaningful fiber tracts, is an essential step to enable tract quantification and visualization. In this study, we present a deep learning tractography segmentation method (DeepWMA) that allows fast and consistent identification of 54 major deep white matter fiber tracts from the whole brain. We create a large-scale training tractography dataset of 1 million labeled fiber samples, and we propose a novel 2D multi-channel feature descriptor (FiberMap) that encodes spatial coordinates of points along each fiber. We learn a convolutional neural network (CNN) fiber classification model based on FiberMap and obtain a high fiber classification accuracy of 90.99% on the training tractography data with ground truth fiber labels. Then, the method is evaluated on a test dataset of 597 diffusion MRI scans from six independently acquired populations across genders, the lifespan (1 day - 82 years), and different health conditions (healthy control, neuropsychiatric disorders, and brain tumor patients). We perform comparisons with two state-of-the-art tract segmentation methods. Experimental results show that our method obtains a highly consistent tract segmentation result, where on average over 99% of the fiber tracts are successfully identified across all subjects under study, most importantly, including neonates and patients with space-occupying brain tumors. We also demonstrate good generalization of the method to tractography data from multiple different fiber tracking methods. The proposed method leverages deep learning techniques and provides a fast and efficient tool for brain white matter segmentation in large diffusion MRI tractography datasets.