Given that the neural and connective tissues of the optic nerve head (ONH) exhibit complex morphological changes with the development and progression of glaucoma, their simultaneous isolation from optical coherence tomography (OCT) images may be of great interest for the clinical diagnosis and management of this pathology. A deep learning algorithm (custom U-NET) was designed and trained to segment 6 ONH tissue layers by capturing both the local (tissue texture) and contextual information (spatial arrangement of tissues). The overall Dice coefficient (mean of all tissues) was 0.91 ± 0.05 when assessed against manual segmentations performed by an expert observer. Further, we automatically extracted six clinically relevant neural and connective tissue structural parameters from the segmented tissues. We offer here a robust segmentation framework that could also be extended to the 3D segmentation of the ONH tissues.