Brain tumour is a serious disease, and the number of people who are dying due to brain tumours is increasing. Manual tumour diagnosis from magnetic resonance images (MRIs) is a time consuming process and is insufficient for accurately detecting, localizing, and classifying the tumour type. This research proposes a novel two-phase multi-model automatic diagnosis system for brain tumour detection and localization. In the first phase, the system structure consists of preprocessing, feature extraction using a convolutional neural network (CNN), and feature classification using the error-correcting output codes support vector machine (ECOC-SVM) approach. The purpose of the first system phase is to detect brain tumour by classifying the MRIs into normal and abnormal images. The aim of the second system phase is to localize the tumour within the abnormal MRIs using a fully designed five-layer region-based convolutional neural network (R-CNN). The performance of the first phase was assessed using three CNN models, namely, AlexNet, Visual Geometry Group (VGG)-16, and VGG-19, and a maximum detection accuracy of 99.55% was achieved with AlexNet using 349 images extracted from the standard Reference Image Database to Evaluate Response (RIDER) Neuro MRI database. The brain tumour localization phase was evaluated using 804 3D MRIs from the Brain Tumor Segmentation (BraTS) 2013 database, and a DICE score of 0.87 was achieved. The empirical work proved the outstanding performance of the proposed deep learning-based system in tumour detection compared to other non-deep-learning approaches in the literature. The obtained results also demonstrate the superiority of the proposed system concerning both tumour detection and localization.