Multi-camera systems are increasingly vital in the environmental perception of autonomous vehicles and robotics. Their physical configuration offers inherent fixed relative pose constraints that benefit Structure-from-Motion (SfM). However, traditional global SfM systems struggle with robustness due to their optimization framework. We propose a novel global motion averaging framework for multi-camera systems, featuring two core components: a decoupled rotation averaging module and a hybrid translation averaging module. Our rotation averaging employs a hierarchical strategy by first estimating relative rotations within rigid camera units and then computing global rigid unit rotations. To enhance the robustness of translation averaging, we incorporate both camera-to-camera and camera-to-point constraints to initialize camera positions and 3D points with a convex distance-based objective function and refine them with an unbiased non-bilinear angle-based objective function. Experiments on large-scale datasets show that our system matches or exceeds incremental SfM accuracy while significantly improving efficiency. Our framework outperforms existing global SfM methods, establishing itself as a robust solution for real-world multi-camera SfM applications. The code is available at https://github.com/3dv-casia/MGSfM/.