Complex distributed software systems are built by connecting software components across a large number of physical or virtual machines. Deploying such systems reliably and efficiently is a difficult task that involves multiple actors. Coordination mechanisms and programming support are needed. In this paper, we introduce Madeus, a component-based model that allows efficient and highly parallel deployment procedures for distributed software through a declarative approach. We describe the formal model of Madeus, its performance prediction model, and its concrete language and prototype. We evaluated Madeus on a complex real-world use case, the deployment of OpenStack, and measured a deployment time reduced by up to 71% compared to existing solutions.