Key message: We propose new methods to predict genotype × environment interaction by selecting relevant environmental covariates and using an AMMI decomposition of the interaction. Abstract: Farmers are asked to produce more efficiently and to reduce their inputs in the context of climate change. They have to face more and more limiting factors that can combine in numerous stress scenarios. One solution to this challenge is to develop varieties adapted to specific environmental stress scenarios. For this, plant breeders can use genomic predictions coupled with environmental characterization to identify promising combinations of genes in relation to stress covariates. One way to do it is to take into account the genetic similarity between varieties and the similarity between environments within a mixed model framework. Molecular markers and environmental covariates (EC) can be used to estimate relevant covariance matrices. In the present study, based on a multi-environment trial of 220 European elite winter bread wheat (Triticum aestivum L.) varieties phenotyped in 42 environments, we compared reference regression models potentially including ECs, and proposed alternative models to increase prediction accuracy. We showed that selecting a subset of ECs, and estimating covariance matrices using an AMMI decomposition to benefit from the information brought by the phenotypic records of the training set are promising approaches to better predict genotype-by-environment interactions (G × E). We found that using a different kinship for the main genetic effect and the G × E effect increased prediction accuracy. Our study also demonstrates that integrative stress indexes simulated by crop growth models are more efficient to capture G × E than climatic covariates.