Livestock production both contributes to and is affected by global climate change, and substantial modifications will be required to increase its climate resilience. In this context, reliance on dominant commercial livestock breeds, featuring small effective population sizes, makes current production strategies vulnerable if their production is restricted to environments, which may be too costly to support under future climate scenarios. The adaptability of animal populations to future environments will therefore become important. To help evaluate the role of genetics in climate adaptation, we compared selection strategies in dairy cattle using breeding simulations, where genomic selection was used on two negatively correlated traits for production (assumed to be moderately heritable) and adaptation (assumed to have low heritability). Compared with within-population breeding, genomic introgression produced a more positive genetic change for both production and adaptation traits. Genomic introgression from highly adapted but low production value populations into highly productive but low adaptation populations was most successful when the adaptation trait was given a lower selection weight than the production trait. Genomic introgression from highly productive population to highly adapted population was most successful when the adaptation trait was given a higher selection weight than the production trait. Both these genomic introgression schemes had the lowest risk of inbreeding. Our results suggest that both adaptation and production can potentially be improved simultaneously by genomic introgression.