This paper presents VGGT-360, a novel training-free framework for zero-shot, geometry-consistent panoramic depth estimation. Unlike prior view-independent training-free approaches, VGGT-360 reformulates the task as panoramic reprojection over multi-view reconstructed 3D models by leveraging the intrinsic 3D consistency of VGGT-like foundation models, thereby unifying fragmented per-view reasoning into a coherent panoramic understanding. To achieve robust and accurate estimation, VGGT-360 integrates three plug-and-play modules that form a unified panorama-to-3D-to-depth framework: (i) Uncertainty-guided adaptive projection slices panoramas into perspective views to bridge the domain gap between panoramic inputs and VGGT's perspective prior. It estimates gradient-based uncertainty to allocate denser views to geometry-poor regions, yielding geometry-informative inputs for VGGT. (ii) Structure-saliency enhanced attention strengthens VGGT's robustness during 3D reconstruction by injecting structure-aware confidence into its attention layers, guiding focus toward geometrically reliable regions and enhancing cross-view coherence. (iii) Correlation-weighted 3D model correction refines the reconstructed 3D model by reweighting overlapping points using attention-inferred correlation scores, providing a consistent geometric basis for accurate panoramic reprojection. Extensive experiments show that VGGT-360 outperforms both trained and training-free state-of-the-art methods across multiple resolutions and diverse indoor and outdoor datasets.