In this work we have investigated the genetic changes underlying the high glutathione (GSH) production showed by the evolved Saccharomyces cerevisiae strain UMCC 2581, selected in a molybdate-enriched environment after sexual recombination of the parental wine strain UMCC 855. To reach our goal, we first generated strains with the desired phenotype, and then we mapped changes underlying adaptation to molybdate by using a whole-genome sequencing. Moreover, we carried out the RNA-seq that allowed an accurate measurement of gene expression and an effective comparison between the transcriptional profiles of parental and evolved strains, in order to investigate the relationship between genotype and high GSH production phenotype. Among all genes evaluated only two genes, MED2 and RIM15 both related to oxidative stress response, presented new mutations in the UMCC 2581 strain sequence and were potentially related to the evolved phenotype. Regarding the expression of high GSH production phenotype, it included over-expression of amino acids permeases and precursor biosynthetic enzymes rather than the two GSH metabolic enzymes, whereas GSH production and metabolism, transporter activity, vacuolar detoxification and oxidative stress response enzymes were probably added resulting in the molybdate resistance phenotype. This work provides an example of a combination of an evolution-based strategy to successful obtain yeast strain with desired phenotype and inverse engineering approach to genetic characterize the evolved strain. The obtained genetic information could be useful for further optimization of the evolved strains and for providing an even more rapid approach to identify new strains, with a high GSH production, through a marked-assisted selection strategy.