Cloud computing accelerates design space exploration in logic synthesis, and parameter tuning in physical design. However, deploying EDA jobs on the cloud requires EDA teams to deeply understand the characteristics of their jobs in cloud environments. Unfortunately, there has been little to no public information on these characteristics. Thus, in this paper, we formulate the problem of migrating EDA jobs to the cloud. First, we characterize the performance of four main EDA applications, namely: synthesis, placement, routing and static timing analysis. We show that different EDA jobs require different machine configurations. Second, using observations from our characterization, we propose a novel model based on Graph Convolutional Networks to predict the total runtime of a given application on different machine configurations. Our model achieves a prediction accuracy of 87%. Third, we develop a new formulation for optimizing cloud deployments in order to reduce deployment costs while meeting deadline constraints. We present a pseudo-polynomial optimal solution using a multi-choice knapsack mapping that reduces costs by 35.29%.