Cloud Computing is the dynamic provisioning of resources to provide services to end-users over the internet. The realization of cloud computing requires addressing several challenges, such as resource discovery, security, scheduling, and load balancing. Among these research issues, load balancing is the most challenging one. Therefore, in the past few years, research into various static and dynamic algorithms to achieve optimal results is gaining importance. This research proposes Swarm Intelligence (SI) as a load-balancing solution for cloud computing. Several alternatives in the literature (like genetic algorithm, ACO, PSO, BAT, GWO and many others) are investigated, but none consider the load balancing convergence time with global optimization. Among these algorithms, this research emphasizes Particle Swarm Optimization (PSO) and GreyWolf Optimization (GWO). A combined approach of GWO-PSO that capitalizes on the benefits of fast convergence and global optimization is proposed in this paper. These two techniques enhance system efficiency and resource allocation, working together to solve the load-balancing challenge. Compared to other traditional approaches, the findings of this research are promising while achieving globally optimized fast convergence and reducing overall response time. On average, the overall response time of the proposed technique is reduced to 12% as compared to other algorithms. Furthermore, the best optimal value obtained from the objective function of the proposed GWO-PSO algorithm improves PSO to 97.253% in terms of convergence.