Grounded theory offers deep insights from qualitative data, but its reliance on expert-intensive manual coding presents a major scalability bottleneck. Existing computational tools either fail on full automation or lack flexible schema construction. We introduce LOGOS, a novel, end-to-end framework that fully automates the grounded theory workflow, transforming raw text into a structured, hierarchical theory. LOGOS integrates LLM-driven coding, semantic clustering, graph reasoning, and a novel iterative refinement process to build highly reusable codebooks. To ensure fair comparison, we also introduce a principled 5-dimensional metric and a train-test split protocol for standardized, unbiased evaluation. Across five diverse corpora, LOGOS consistently outperforms strong baselines and achieves a remarkable average $80.4\%$ alignment with an expert-developed schema on complex datasets. LOGOS demonstrates a potential to democratize and scale qualitative research without sacrificing theoretical nuance.