Relocation is a large-scale mutation event that places genes in new genomic locations and chromatin environments. Consequently, a relocated gene may incur novel expression patterns and such changes are widely hypothesized to drive evolutionary divergence and speciation. Here, we design the first methods for predicting evolutionary divergence and its underlying parameters from expression data of relocated genes. In particular, our methods utilize random forests, support vector machines, and multi-layer neural networks built on a model of gene expression evolution. Application of our methods to simulated data shows that, whereas the globally best performance is achieved with a neural network, all architectures have high power and accuracy in predicting evolutionary divergence and its underlying parameters across a diversity of evolutionary scenarios. Further, application of our methods to empirical data from Drosophila shows that evolutionary divergence occurs in 15-20% of relocated genes, is driven by both neutral and selective forces, and tends to affect genes involved in development. Thus, by providing a mechanism for assaying whether and how evolutionary divergence occurs after gene relocations, our suite of machine learning methods represents a major advancement in studying the roles of gene relocations in the origins of novel functions, phenotypes, and species.