Purpose: Accurate regional segmentation of the prostate boundaries on magnetic resonance (MR) images is a fundamental requirement before automated prostate cancer diagnosis can be achieved. In this paper, we describe a novel methodology to segment prostate whole gland (WG), central gland (CG), and peripheral zone (PZ), where PZ + CG = WG, from T2W and apparent diffusion coefficient (ADC) map prostate MR images. Methods: We designed two similar models each made up of two U-Nets to delineate the WG, CG, and PZ from T2W and ADC map MR images, separately. The U-Net, which is a modified version of a fully convolutional neural network, includes contracting and expanding paths with convolutional, pooling, and upsampling layers. Pooling and upsampling layers help to capture and localize image features with a high spatial consistency. We used a dataset consisting of 225 patients (combining 153 and 72 patients with and without clinically significant prostate cancer) imaged with multiparametric MRI at 3 Tesla. Results and conclusion: Our proposed model for prostate zonal segmentation from T2W was trained and tested using 1154 and 1587 slices of 100 and 125 patients, respectively. Median of Dice similarity coefficient (DSC) on test dataset for prostate WG, CG, and PZ were 95.33 AE 7.77%, 93.75 AE 8.91%, and 86.78 AE 3.72%, respectively. Designed model for regional prostate delineation from ADC map images was trained and validated using 812 and 917 slices from 100 and 125 patients. This model yielded a median DSC of 92.09 AE 8.89%, 89.89 AE 10.69%, and 86.1 AE 9.56% for prostate WG, CG, and PZ on test samples, respectively. Further investigation indicated that the proposed algorithm reported high DSC for prostate WG segmentation from both T2W and ADC map MR images irrespective of WG size. In addition, segmentation accuracy in terms of DSC does not significantly vary among patients with or without significant tumors. Significance: We describe a method for automated prostate zonal segmentation using T2W and ADC map MR images independent of prostate size and the presence or absence of tumor. Our results are important in terms of clinical perspective as fully automated methods for ADC map images, which are considered as one of the most important sequences for prostate cancer detection in the PZ and CG, have not been reported previously.