Drones, or unmanned aerial vehicles, can be used for commercial services such as short-distance delivery. In order to ensure quality services, multiple drone-based delivery service providers can be employed in delivery service systems. In this article, we address two very important and unexplored challenges of employing drones in delivery services. First, involving multiple drones from different service providers elevates the chance of collision during flights. Second, drones may hamper the privacy of citizens by unauthorized access to private and restricted areas. In order to solve the aforementioned issues, we propose a blockchain-based policy enforcement mechanism in the drone-based delivery service systems. At first, the mechanism will set policies to establish pre-allocated flight paths for different drones at different times to avoid collisions, and ensure the privacy of citizens by restricting their access to unauthorized areas. Later, the blockchain will enforce the policies to monitor compliance of the drone flights and identify non-compliant drone services to penalize corresponding service providers. We simulate a virtual drone-based delivery system with the Ethereum blockchain platform and examine the performance and feasibility of our proposed mechanism.