In the Internet of Things (IoT) era, blockchain-enhanced edge services have emerged as a promising paradigm to process and secure the massive data generated by IoT devices. However, the extra resources and processing time taken up by the blockchain cannot be ignored, which poses a greater challenge to the task offloading problem for the service. Motivated by this, this paper proposes a more efficient fusion framework, FBMTO, which fully considers the balance between additional costs and performance improvements for task offloading in edge computing. The framework transforms the task offloading problem into a dual-objective optimization problem by fully considering the costs produced by the on-chain tasks. Then, we design a Blockchain-enabled Multi-Agent Reinforcement learning Task Offloading algorithm (BMARTO) to find the optimal offloading decision. In BMARTO, a novel reputation mechanism is introduced to speed up the optimization process while maintaining efficiency in the task offloading process. Additionally, we design an Edge-Computing Delegated Proof of Stake consensus algorithm (ECDPoS), an improved Delegated Proof of Stake (DPoS) that enabling high-throughput consensus operations in edge environments and boosting blockchain efficiency via a novel smart contract. Experimental results demonstrate that FBMTO reduces task latency and energy consumption while ensuring data security, outperforming existing methods in various scenarios.