As an important supplement to ground computing, edge computing can effectively alleviate the computational burden on ground systems. In the context of integrating edge computing with low-Earth-orbit satellite networks, this paper proposes an edge computing task offloading algorithm based on distributed multi-agent deep reinforcement learning (DMADRL) to address the challenges of task offloading, including low transmission rates, low task completion rates, and high latency. Firstly, a Ground–UAV–LEO (GUL) three-layer architecture is constructed to improve offloading transmission rate. Secondly, the task offloading problem is decomposed into two sub-problems: offloading decisions and resource allocation. The former is addressed using a distributed multi-agent deep Q-network, where the problem is formulated as a Markov decision process. The Q-value estimation is iteratively optimized through the online and target networks, enabling the agent to make autonomous decisions based on ground and satellite load conditions, utilize the experience replay buffer to store samples, and achieve global optimization via global reward feedback. The latter employs the gradient descent method to dynamically update the allocation strategy based on the accumulated task data volume and the remaining resources, while adjusting the allocation through iterative convergence error feedback. Simulation results demonstrate that the proposed algorithm increases the average transmission rate by 21.7%, enhances the average task completion rate by at least 22.63% compared with benchmark algorithms, and reduces the average task processing latency by at least 11.32%, thereby significantly improving overall system performance.