Cloud computing has been a cost-efficient paradigm for deploying various applications in datacenters in recent years. Therefore, efficient provisioning for virtual data center (VDC) requests from different service providers (SPs) over physical data centers plays a vital role in improving the quality of service (QoS) and reducing the operational cost of SPs. Therefore, a significant attention has been paid for the VDC provisioning problem. However, few approaches have been proposed for the problem of reliable VDC embedding across multiple data centers, as most of them only consider the problem of VDC mapping within a single data center. In this paper, we study the problem of QoS-aware VDC provisioning across multiple data centers, such that the total bandwidth consumption in the inter-data center backbone network is minimized while satisfying the reliability requirement of each VDC request. We formulate this problem as a mathematical optimization problem by using integer linear programming (ILP) and propose an efficient heuristic algorithm called reliable VDC embedding (RVDCE) algorithm to solve this NP-hard problem. The simulation results show that the proposed algorithm performs better in terms of blocking ratio, CPU resource consumption, and bandwidth consumption of backbone network than the existing solution. In addition, this paper has also incorporated integrated security to minimize security vulnerabilities seen in other similar approaches. Apart from demonstrating how to resolve security challenges in our VDC proposal, cost calculations have been implemented to demonstrate the robustness, resiliency, validity, and effectiveness of the VDC provisioning solution for cloud computing.