In the realm of mobile edge computing (MEC), efficient computation task offloading plays a pivotal role in ensuring a seamless quality of experience (QoE) for users. Maintaining a high QoE is paramount in today's interconnected world, where users demand responsive and reliable services. This challenge stands as one of the most primary key factors contributing to handling dynamic and uncertain mobile environment. In this study, we delve into computation offloading in MEC systems, where strict task processing deadlines and energy constraints can adversely affect the system performance. We formulate the computation task offloading problem as a Markov decision process (MDP) to maximize the long-term QoE of each user individually. We propose a decentralized QoE-oriented computation offloading (QOCO) algorithm based on deep reinforcement learning (DRL) that empowers mobile devices to make their offloading decisions without requiring knowledge of decisions made by other devices. Through numerical studies, we evaluate the performance of QOCO. Simulation results validate that the QOCO algorithm efficiently exploits the computational resources of edge nodes. Consequently, it can complete 14% more tasks and reduce task delay and energy consumption by 9% and 6%, respectively. These together contribute to a significant improvement of at least 37% in average QoE compared to an existing algorithm.