Gene regulatory networks (GRNs) describe regulatory relationships between transcription factors (TFs) and their target genes. Computational methods to infer GRNs typically combine evidence across different conditions to infer context-agnostic networks. We develop a method, Network Reprogramming using EXpression (NetREX), that constructs a context-specific GRN given context-specific expression data and a context-agnostic prior network. NetREX remodels the prior network to obtain the topology that provides the best explanation for expression data. Because NetREX utilizes prior network topology, we also develop PriorBoost, a method that evaluates a prior network in terms of its consistency with the expression data. We validate NetREX and PriorBoost using the "gold standard" E. coli GRN from the DREAM5 network inference challenge and apply them to construct sex-specific Drosophila GRNs. NetREX constructed sex-specific Drosophila GRNs that, on all applied measures, outperform networks obtained from other methods indicating that NetREX is an important milestone toward building more accurate GRNs.