Federated learning (FL) enables multiple participants to collaboratively train machine learning models while ensuring their data remains private and secure. Blockchain technology further enhances FL by providing stronger security, a transparent audit trail, and protection against data tampering and model manipulation. Most blockchain-secured FL systems rely on conventional consensus mechanisms: Proof-of-Work (PoW) is computationally expensive, while Proof-of-Stake (PoS) improves energy efficiency but risks centralization as it inherently favors participants with larger stakes. Recently, learning-based consensus has emerged as an alternative by replacing cryptographic tasks with model training to save energy. However, this approach introduces potential privacy vulnerabilities, as the training process may inadvertently expose sensitive information through gradient sharing and model updates. To address these challenges, we propose a novel Zero-Knowledge Proof of Training (ZKPoT) consensus mechanism. This method leverages the zero-knowledge succinct non-interactive argument of knowledge proof (zk-SNARK) protocol to validate participants' contributions based on their model performance, effectively eliminating the inefficiencies of traditional consensus methods and mitigating the privacy risks posed by learning-based consensus. We analyze our system's security, demonstrating its capacity to prevent the disclosure of sensitive information about local models or training data to untrusted parties during the entire FL process. Extensive experiments demonstrate that our system is robust against privacy and Byzantine attacks while maintaining accuracy and utility without trade-offs, scalable across various blockchain settings, and efficient in both computation and communication.