Recent advancements in Large Language Models (LLMs) have sparked a revolution across many research fields. In robotics, the integration of common-sense knowledge from LLMs into task and motion planning has drastically advanced the field by unlocking unprecedented levels of context awareness. Despite their vast collection of knowledge, large language models may generate infeasible plans due to hallucinations or missing domain information. To address these challenges and improve plan feasibility and computational efficiency, we introduce DELTA, a novel LLM-informed task planning approach. By using scene graphs as environment representations within LLMs, DELTA achieves rapid generation of precise planning problem descriptions. To enhance planning performance, DELTA decomposes long-term task goals with LLMs into an autoregressive sequence of sub-goals, enabling automated task planners to efficiently solve complex problems. In our extensive evaluation, we show that DELTA enables an efficient and fully automatic task planning pipeline, achieving higher planning success rates and significantly shorter planning times compared to the state of the art. Project webpage: https://delta-llm.github.io/