Multi-access Edge Computing (MEC) is a standard network architecture of edge computing, which is proposed to handle tremendous computation demands of emerging resource-intensive and latency-sensitive applications and services and accommodate Quality of Service (QoS) requirements for ever-growing users through computation offloading. Since the demand of end-users is unknown in a rapidly changing dynamic environment, processing offloaded tasks in a non-optimal server can deteriorate QoS due to high latency and increasing task failures. In order to deal with such a challenge in MEC, a two-stage Belief Rule-Based (BRB) workload orchestrator is proposed to distribute the workload of end-users to optimum computing units, support strict QoS requirements, ensure efficient utilization of computational resources, minimize task failures, and reduce the overall service time. The proposed BRB workload orchestrator decides the optimal execution location for each offloaded task from User Equipment (UE) within the overall MEC architecture based on network conditions, computational resources, and task requirements. EdgeCloudSim simulator is used to conduct comprehensive simulation experiments for evaluating the performance of the proposed BRB orchestrator in contrast to four workload orchestration approaches from the literature with different types of applications. Based on the simulation experiments, the proposed workload orchestrator outperforms state-of-the-art workload orchestration approaches and ensures efficient utilization of computational resources while minimizing task failures and reducing the overall service time.