In order to improve operational efficiency and agility in contemporary IT systems, this study investigates the integration of DevOps methods with cloud management. It offers a thorough rundown of the main DevOps tools and technologies needed to manage cloud infrastructure, including as monitoring systems, CI/CD pipelines, Infrastructure as Code (IaC) tools, and configuration management systems. The inability to allow concurrent project development and deployment on the same operational infrastructure (such as a cluster of Docker containers) is a practical shortcoming of current DevOps systems. In order to fill the gaps in the current Development and Operations (DevOps) methods, this paper offers a thorough study and explores how such integrations in Amazon Web Services might enhance deployment efficiency, dependability in software and infrastructure delivery, and security. Thus, the goal of this research is to use the AWS platform to automate the processes of developing and maintaining IT infrastructure. Therefore, we provide a mathematical model in this research to ascertain the ideal arrangement for IT infrastructure. This study investigates in detail how Kubernetes clusters in the AWS environment may be efficiently automated, scaled, and managed using Terraform, an Infrastructure as Code (IaC) tool. It thoroughly examines the advantages of using Terraform, highlighting how it may enhance productivity, automation, scalability, and security while managing Kubernetes clusters. To demonstrate Terraform's capabilities in infrastructure management, the paper contrasts it with other popular (IaC) tools and techniques. It also explores how Terraform works with AWS services to streamline procedures and cut down on complexity. Trends and possible developments in combining Kubernetes and Terraform to improve the administration of cloud-native apps are also covered in the paper.