Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) plays an important role in diagnosis and grading of brain tumor. Although manual DCE biomarker extraction algorithms boost the diagnostic yield of DCE-MRI by providing quantitative information on tumor prognosis and prediction, they are time-consuming and prone to human error. In this paper, we propose a fully-automated, end-to-end system for DCE-MRI analysis of brain tumors. Our deep learning-powered technique does not require any user interaction, it yields reproducible results, and it is rigorously validated against benchmark (BraTS'17 for tumor segmentation, and a test dataset released by the Quantitative Imaging Biomarkers Alliance for the contrast-concentration fitting) and clinical (44 low-grade glioma patients) data. Also, we introduce a cubic model of the vascular input function used for pharmacokinetic modeling which significantly decreases the fitting error when compared with the state of the art, alongside a real-time algorithm for determination of the vascular input region. An extensive experimental study, backed up with statistical tests, showed that our system delivers state-of-the-art results (in terms of segmentation accuracy and contrast-concentration fitting) while requiring less than 3 minutes to process an entire input DCE-MRI study using a single GPU.