This work presents a meta-reinforcement learning approach to develop a universal locomotion control policy capable of zero-shot generalization across diverse quadrupedal platforms. The proposed method trains an RL agent equipped with a memory unit to imitate reference motions using a small set of procedurally generated quadruped robots. Through comprehensive simulation and real-world hardware experiments, we demonstrate the efficacy of our approach in achieving locomotion across various robots without requiring robot-specific fine-tuning. Furthermore, we highlight the critical role of the memory unit in enabling generalization, facilitating rapid adaptation to changes in the robot properties, and improving sample efficiency.