Abstract: Task and motion planning (TAMP) for multi-robot systems, combining discrete task planning with continuous motion planning, presents a significant challenge in robotics. Current TAMP methodologies, which typically rely on sampling-based or optimization-based approaches, often fail to effectively scale to multi-robot systems with complex specifications, resulting in infeasible solutions and extended solve times. In this paper, we address the hierarchical temporal logic TAMP problem for multi-robot systems, where complex tasks are defined using expressive hierarchical temporal logic specifications, and task assignments to individual robots are not predetermined. We introduce an efficient convex-optimization-based method that incorporates hierarchical temporal logic TAMP within a hybrid Graph of Convex Sets (GCS) framework. This framework enables simultaneous consideration of both the discrete task level and the continuous motion level and is proven to be sound and complete. To reduce the complexity of the GCS framework, we apply multiple heuristics to prune the graph, thereby reducing optimization time. Using a multi-robot cooperative pick-and-place task as a case study, we incorporate handover constraints into the hybrid GCS framework and address the optimization using mixed-integer convex programming (MICP). Our evaluations, conducted on various high-dimensional multi-robot systems in both simulated and real-world environments—including quadrupeds, robotic arms, and automated conveyor systems—demonstrate that our method surpasses existing approaches in terms of execution time and optimality. We also demonstrate that our method scales effectively with the complexity of tasks.