Brain tumors are considered one of the most serious, prominent and life-threatening diseases globally. Brain tumors cause thousands of deaths every year around the globe because of the rapid growth of tumor cells. Therefore, timely analysis and automatic detection of brain tumors are required to save the lives of thousands of people around the globe. Recently, deep transfer learning (TL) approaches are most widely used to detect and classify the three most prominent types of brain tumors, i.e., glioma, meningioma and pituitary. For this purpose, we employ state-of-the-art pre-trained TL techniques to identify and detect glioma, meningioma and pituitary brain tumors. The aim is to identify the performance of nine pre-trained TL classifiers, i.e., Inceptionresnetv2, Inceptionv3, Xception, Resnet18, Resnet50, Resnet101, Shufflenet, Densenet201 and Mobilenetv2, by automatically identifying and detecting brain tumors using a fine-grained classification approach. For this, the TL algorithms are evaluated on a baseline brain tumor classification (MRI) dataset, which is freely available on Kaggle. Additionally, all deep learning (DL) models are fine-tuned with their default values. The fine-grained classification experiment demonstrates that the inceptionresnetv2 TL algorithm performs better and achieves the highest accuracy in detecting and classifying glioma, meningioma and pituitary brain tumors, and hence it can be classified as the best classification algorithm. We achieve 98.91% accuracy, 98.28% precision, 99.75% recall and 99% F-measure values with the inceptionresnetv2 TL algorithm, which out-performs the other DL algorithms. Additionally, to ensure and validate the performance of TL classifiers, we compare the efficacy of the inceptionresnetv2 TL algorithm with hybrid approaches, in which we use convolutional neural networks (CNN) for deep feature extraction and a Support Vector Machine (SVM) for classification. Similarly, the experiment’s results show that TL algorithms, and inceptionresnetv2 in particular, out-perform the state-of-the-art DL algorithms in classifying brain MRI images into glioma, meningioma, and pituitary. The hybrid DL approaches used in the experiments are Mobilnetv2, Densenet201, Squeeznet, Alexnet, Googlenet, Inceptionv3, Resnet50, Resnet18, Resnet101, Xception, Inceptionresnetv3, VGG19 and Shufflenet.