The quick pace of quantum computing threatens classical cryptographic practices immensely, requiring quantum-resistant security solutions. This paper discusses the integration of Quantum Key Distribution (QKD) based on the BB84 protocol with AES-256 encryption to provide more secure cloud-based data storage. QKD, based on quantum mechanics principles, provides secure key exchange by making eavesdropping attempts detectable, thus ensuring unconditional security. The suggested framework appears to address weaknesses in traditional encryption methods by featuring a hybrid cryptographic model under which QKD securely distributes the encryption keys and AES-256 secures stored data. The research presents a step-by-step approach from system design, technical implementation, performance assessment, and prototype testing. Experimental findings, provided by QKDNetSim, confirm the usability of the new system by producing a low Quantum Bit Error Rate (QBER) of 3%, the rate of key generation of 1 million bits per second, and negligible latency of 0.05036 s. Encryption efficiency is enormously enhanced, and optimized AES-256 encryption speeds up processing time to 0.05 s per gigabyte. In addition, the system has a high throughput of 19.85 GB per second, making it scalable and viable for use in cloud environments. Performance testing under an emulated cloud infrastructure assures the effectiveness of the integration to counter quantum threats while ensuring real-time data protection. Through the combination of quantum security and classical encryption, the method provides a secure, quantum-resistant framework applicable to contemporary cloud-based applications. The results emphasize the need to implement QKD as a countermeasure against quantum computing attacks and provide an industrial-strength, scalable security solution for cloud data protection.