This paper proposes a spatiotemporal (ST) fusion framework robust against diverse noise for satellite images, named Temporally-Similar Structure-Aware ST fusion (TSSTF). ST fusion is a promising approach to address the trade-off between the spatial and temporal resolution of satellite images. In real-world scenarios, observed satellite images are severely degraded by noise due to measurement equipment and environmental conditions. Consequently, some recent studies have focused on enhancing the robustness of ST fusion methods against noise. However, existing noise-robust ST fusion approaches often fail to capture fine spatial structure, leading to oversmoothing and artifacts. To address this issue, TSSTF introduces two key mechanisms: Temporally-Guided Total Variation (TGTV) and Temporally-Guided Edge Constraint (TGEC). TGTV is a weighted total variation-based regularization that promotes spatial piecewise smoothness while preserving structural details, guided by a reference high spatial resolution image acquired on a nearby date. TGEC enforces consistency in edge locations between two temporally adjacent images, while allowing for spectral variations. We formulate the ST fusion task as a constrained optimization problem incorporating TGTV and TGEC, and develop an efficient algorithm based on a preconditioned primal-dual splitting method. Experimental results demonstrate that TSSTF performs comparably to state-of-the-art methods under noise-free conditions and outperforms them under noisy conditions.