<p>Cloud computing has become the foundation of modern IT services, providing on-demand and scalable distribution of computing resources. Nevertheless, this task scheduling and resource allocation problem is non-trivial since the nature of the workloads is dynamic and heterogeneous. Classical scheduling algorithms, such as round-robin or heuristic solutions, do not adjust to workload variations and, as a result, lead to underutilized resources and an overall increase in SLA (service level agreement) violations. As a means of overcoming them, this paper introduces a hybrid scheduling framework composed of two parts, namely Eagle Strategy (ES), a metaheuristics algorithm that combines the advantages of global exploration and local exploitation, and Deep Q-Learning (DQL), which can adapt a policy based on its experience over a high-dimensional distribution of experiences and actions. The resulting Eagle-DQL model blends stochastic Lévy flights and Gaussian local search to improve exploration and the DQL component learns adaptive allocation policies by interacting with the environment. The model is simulated on a cloud with the use of task queues and a VM-pool simulated using Google Cluster Traces. Experiment results show that Eagle-DQL can reduce task completion time by 37%, violations in SLA by 80%, and increase the VM utilization by 15%, whilst decreasing VM switching overhead compared to baselines of Random, Round Robin, ES-only, and DQL-only settings. The findings show that the proposed framework presents a scalable and adaptive SLA-aware Schedule framework in cloud infrastructures.</p>