Drug repurposing refers to the process of discovering new therapeutic uses for existing medicines. Compared to traditional drug discovery, drug repurposing is attractive for its speed, cost, and reduced risk of failure. However, existing approaches for drug repurposing involve complex, computationally-intensive analytical methods that are not widely used in practice. Instead, repurposing decisions are often based on subjective judgments from limited empirical evidence. In this article, we develop a novel Bayesian network meta-analysis (NMA) framework that can predict the efficacy of an approved treatment in a new indication and thereby identify candidate treatments for repurposing. We obtain predictions using two main steps: first, we use standard NMA modeling to estimate average relative effects from a network comprised of treatments studied in both indications in addition to one treatment studied in only one indication. Then, we model the correlation between relative effects using various strategies that differ in how they model treatments across indications and within the same drug class. We evaluate the predictive performance of each model using a simulation study and find that the model minimizing root mean squared error of the posterior median for the candidate treatment depends on the amount of available data, the level of correlation between indications, and whether treatment effects differ, on average, by drug class. We conclude by discussing an illustrative example in psoriasis and psoriatic arthritis and find that the candidate treatment has a high probability of success in a future trial.