Delineation and quantification of normal and abnormal brain tissues on Magnetic Resonance Images is fundamental to the diagnosis and longitudinal assessment of neurological diseases. Here we sought to develop a convolutional neural network for automated multiclass tissue segmentation of brain MRIs that was robust at typical clinical resolutions and in the presence of a variety of lesions. We trained a 3D U-Net for full brain multiclass tissue segmentation from a prior atlas-based segmentation method on an internal dataset that consisted of 558 clinical T1-weighted brain MRIs (453/52/53; training/validation/test) of patients with one of 50 different diagnostic entities (n = 362) or with a normal brain MRI (n = 196). We then used transfer learning to refine our model on an external dataset that consisted of 7 patients with hand-labeled tissue types. We evaluated the tissue-wise and intra-lesion performance with different loss functions and spatial prior information in the validation set and applied the best performing model to the internal and external test sets. The network achieved an average overall Dice score of 0.87 and volume similarity of 0.97 in the internal test set. Further, the network achieved a median intra-lesion tissue segmentation accuracy of 0.85 inside lesions within white matter and 0.61 inside lesions within gray matter. After transfer learning, the network achieved an average overall Dice score of 0.77 and volume similarity of 0.96 in the external dataset compared to human raters. The network had equivalent or better performance than the original atlas-based method on which it was trained across all metrics and produced segmentations in a hundredth of the time. We anticipate that this pipeline will be a useful tool for clinical decision support and quantitative analysis of clinical brain MRIs in the presence of lesions.