Vision-Language Models (VLMs) in remote sensing often fail at complex analytical tasks, a limitation stemming from their end-to-end training paradigm that bypasses crucial reasoning steps and leads to unverifiable outputs. To address this limitation, we introduce the Perceptually-Grounded Geospatial Chain-of-Thought (Geo-CoT), a framework that models remote sensing analysis as a verifiable, multi-step process. We instill this analytical process through a two-stage alignment strategy, leveraging Geo-CoT380k, the first large-scale dataset of structured Geo-CoT rationales. This strategy first employs supervised fine-tuning (SFT) to instill the foundational cognitive architecture, then leverages Group Reward Policy Optimization (GRPO) to refine the model's reasoning policy towards factual correctness. The resulting model, RSThinker, outputs both a final answer and its justifying, verifiable analytical trace. This capability yields dominant performance, significantly outperforming state-of-the-art models across a comprehensive range of tasks. The public release of our Geo-CoT380k dataset and RSThinker model upon publication serves as a concrete pathway from opaque perception towards structured, verifiable reasoning for Earth Observation.