As organizations transition from on-premises infrastructure to cloud environments, accurately predicting and managing cloud costs becomes a critical concern. Traditional methods of cloud cost modeling and budget forecasting are often based on static rules and historical usage data, leading to inaccuracies and inefficiencies. To address these challenges, AI-assisted cloud cost modeling and budget forecasting have emerged as transformative solutions, offering enhanced precision and adaptability both before and after migration to the cloud. This paper explores the role of artificial intelligence (AI) in improving cloud cost management, with a specific focus on pre-and post-migration scenarios. The AI models discussed leverage machine learning (ML) and data analytics to analyze large sets of data, including historical consumption patterns, resource utilization, and usage trends. By predicting future cloud resource needs based on these insights, AI-driven models help organizations develop more accurate pre-migration cost estimates, enabling better decision-making in the early stages of the cloud adoption journey. In the pre-migration phase, AI-assisted tools analyze the on-premises infrastructure, identify workloads suitable for the cloud, and model cost scenarios based on cloud provider pricing structures (IaaS, PaaS, SaaS). These models also assist in optimizing resource allocation, allowing for the creation of tailored migration strategies that consider both cost-efficiency and performance. Post-migration, AI-based cost forecasting tools continue to offer significant value by providing dynamic, real-time tracking and forecasting of cloud expenses. AI-powered algorithms take into account various factors such as changing usage patterns, fluctuating demand, and pricing changes by cloud providers, delivering accurate cost predictions that help avoid budget overruns. Furthermore, AI-driven optimization strategies allow for continuous monitoring and adjustment of resources, ensuring that organizations maintain optimal cloud spending while maximizing performance. Key benefits of AI-assisted cloud cost modeling and budget forecasting include enhanced accuracy, proactive cost management, the ability to scale resources dynamically, and the reduction of unforeseen expenditures. By leveraging AI in both pre-and post-migration phases, organizations are equipped with the tools necessary to manage their cloud environments efficiently, optimize resource usage, and maintain budgetary control throughout the cloud lifecycle. This research highlights several case studies that demonstrate the practical application of AI-driven cloud cost forecasting tools and the measurable impact on cost reduction, efficiency, and resource optimization post-migration. Furthermore, the paper outlines the key challenges, including data privacy concerns, AI model transparency, and the need for continuous learning and adaptation as cloud environments evolve. Overall, AI-assisted cloud cost modeling and budget forecasting offer organizations a robust framework for achieving better financial control over their cloud environments, thereby empowering more sustainable and scalable cloud adoption strategies.