Brain tumor analysis is essential to the timely diagnosis and effective treatment of patients. Tumor analysis is challenging because of tumor morphology factors like size, location, texture, and heteromorphic appearance in medical images. In this regard, a novel two-phase deep learning-based framework is proposed to detect and categorize brain tumors in magnetic resonance images (MRIs). In the first phase, a novel deep-boosted features space and ensemble classifiers (DBFS-EC) scheme is proposed to effectively detect tumor MRI images from healthy individuals. The deep-boosted feature space is achieved through customized and well-performing deep convolutional neural networks (CNNs), and consequently, fed into the ensemble of machine learning (ML) classifiers. While in the second phase, a new hybrid features fusion-based brain-tumor classification approach is proposed, comprised of both static and dynamic features with an ML classifier to categorize different tumor types. The dynamic features are extracted from the proposed brain region-edge net (BRAIN-RENet) CNN, which is able to learn the heteromorphic and inconsistent behavior of various tumors. In contrast, the static features are extracted by using a histogram of gradients (HOG) feature descriptor. The effectiveness of the proposed two-phase brain tumor analysis framework is validated on two standard benchmark datasets, which were collected from Kaggle and Figshare and contain different types of tumors, including glioma, meningioma, pituitary, and normal images. Experimental results suggest that the proposed DBFS-EC detection scheme outperforms the standard and achieved accuracy (99.56%), precision (0.9991), recall (0.9899), F1-Score (0.9945), MCC (0.9892), and AUC-PR (0.9990). The classification scheme, based on the fusion of feature spaces of proposed BRAIN-RENet and HOG, outperform state-of-the-art methods significantly in terms of recall (0.9913), precision (0.9906), accuracy (99.20%), and F1-Score (0.9909) in the CE-MRI dataset.