One of the major issues in plant breeding is the occurrence of genotype × environment (GE) interaction. Several models have been created to understand this phenomenon and explore it. In the genomic era, several models were employed to improve selection by using markers and account for GE interaction simultaneously. Some of these models use special genetic covariance matrices. In addition, the scale of multi-environment trials is getting larger, and this increases the computational challenges. In this context, we propose an R package that, in general, allows building GE genomic covariance matrices and fitting linear mixed models, in particular, to a few genomic GE models. Here we propose two functions: one to prepare the genomic kernels accounting for the genomic GE and another to perform genomic prediction using a Bayesian linear mixed model. A specific treatment is given for sparse covariance matrices, in particular, to block diagonal matrices that are present in some GE models in order to decrease the computational demand. In empirical comparisons with Bayesian Genomic Linear Regression (BGLR), accuracies and the mean squared error were similar; however, the computational time was up to five times lower than when using the classic approach. Bayesian Genomic Genotype × Environment Interaction (BGGE) is a fast, efficient option for creating genomic GE kernels and making genomic predictions.