With the technological evolution and new applications, user equipment (UEs) has become a vital part of our lives. However, limited computational capabilities and finite battery life bottleneck the performance of computationally demanding applications. A practical solution to enhance the quality of experience (QoE) is to offload the extensive computation to the mobile edge cloud (MEC). Moreover, the network’s performance can be further improved by deploying an unmanned aerial vehicle (UAV) integrated with intelligent reflective surfaces (IRS): an effective alternative to massive antenna systems to enhance the signal quality and suppress interference. In this work, the MEC network architecture is assisted by UAV-IRS to provide computational services to the UEs. To do so, a cost minimization problem in terms of computing time and hovering energy consumption is formulated. Furthermore, to achieve an efficient solution to a formulated challenging problem, the original optimization problem is decoupled into sub-problems using the block-coordinate decent method. Moreover, numerical results are compared to baseline schemes to determine the effectiveness of the proposed scheme. Simulation results demonstrate that the optimal allocation of local computational resources results in minimizing tasks’ computational time and hovering energy consumption.