The adoption of Artificial Intelligence (AI) is now widespread in Information Technology (IT) support. A particular area of interest is in the automation of IT incident management (i.e., the handling of an unusual event that hampers the quality of IT services in the most optimized manner). In this paper, we propose a framework using state-of-art algorithms to classify and predict the severity of such incidents (commonly labeled as High, Medium, and Low severity). We argue that the proposed framework would accelerate the process of handling IT incidents with improved accuracy. The experimentation was performed on the IT Service Management (ITSM) dataset containing 500,000 real-time incident descriptions with their encoded labels (Dataset 1) from a reputable IT firm. Our results showed that the Transformer models outperformed machine learning (ML) and other deep learning (DL) models with a 98% AUC score to predict the three severity classes. We tested our framework with an open-access dataset (Dataset 2) to further validate our findings. Our framework produced a 44% improvement in AUC score compared to the existing benchmark approaches. The results show the plausibility of AI algorithms in automating the prioritization of incident processing in large IT systems.