Embodied planning requires agents to make coherent multi-step decisions based on dynamic visual observations and verbal goals. While recent vision-language models (VLMs) excel at static perception tasks, they struggle in interactive environments. Reinforcement learning (RL) offers a natural way to address this limitation, yet online RL approaches suffer from costly interaction and sparse rewards in embodied settings. This paper introduces ORBIT, an On-policy Reinforcement fine-tuning (RFT) framework with offline rewards for EmBodIed Task Planning, that preserves the generalization benefits of RFT while addressing the challenges of costly interaction and sparse rewards, supported by solid theoretical guarantees. Our approach is evaluated on EmbodiedBench, a recent benchmark for interactive embodied tasks, covering both in-domain and out-of-domain scenarios. Experimental results show that ORBIT achieves SOTA performance on EB-ALFRED, outperforming all closed-source and online-RL-based methods, while being substantially more efficient in training speed and computational cost, remaining robust to sub-optimal expert trajectories, and exhibiting strong generalization to unseen environments. We released all code and data at https://github.com/mail-taii/Reinforced-Reasoning-for-Embodied-Planning.