Rising global temperatures, stronger hydrological cycles, and an increase in the frequency of extreme weather events are all signs of climate change, which is one of the biggest worldwide issues of the twenty-first century. Computational methods that can process huge heterogeneous datasets and model nonlinear interactions are necessary to address these complicated climate dynamics. Traditional methods of climate modeling, such statistical regression and physics-based numerical simulations, offer significant theoretical insights, but they frequently have issues with high-dimensional data assimilation and computing scalability. New possibilities for improving climate prediction accuracy and enabling data-driven climate analytics have been made possible by recent developments in artificial intelligence (AI), notably machine learning and deep learning. A PRISMA-aligned systematic review of AI methods used for climate change prediction and mitigation between 2020 and 2026 is presented in this work. 120 peer-reviewed publications in all were examined from a variety of angles, including data sources, model architecture, learning paradigm, application domain, and assessment measures. The findings show that AI-driven climate research is expanding quickly, with prediction-oriented applications making up around 70% of the literature and mostly concentrating on extreme weather detection, precipitation modeling, and temperature forecasting. Due to their capacity to capture intricate spatiotemporal climatic patterns, deep learning architectures like Long Short-Term Memory (LSTM), Convolutional Neural Networks (CNN), transformers, and graph neural networks dominate current research. The paper suggests a four-dimensional taxonomy based on application domain, learning paradigm, data modality, and model architecture to arrange the disjointed research landscape. Critical issues include dataset imbalance, uneven benchmarking procedures, worries about computational sustainability, and a lack of real-world mitigation application are also identified by the review. The results emphasize the need for energy-efficient, scalable, and comprehensible AI systems that can assist realistic approaches to climate adaptation and mitigation.