Identification of loci or genes under natural selection is important for both understanding the genetic basis of local adaptation and practical applications, and genome scans provide a powerful means for such identification purposes. In this study, genome-wide simple sequence repeats markers (SSRs) were used to scan for molecular footprints of divergent selection in Eucalyptus grandis, a hardwood species occurring widely in costal areas from 32° S to 16° S in Australia. High population diversity levels and weak population structure were detected with putatively neutral genomic SSRs. Using three FST outlier detection methods, a total of 58 outlying SSRs were collectively identified as loci under divergent selection against three non-correlated climatic variables, namely, mean annual temperature, isothermality and annual precipitation. Using a spatial analysis method, nine significant associations were revealed between FST outlier allele frequencies and climatic variables, involving seven alleles from five SSR loci. Of the five significant SSRs, two (EUCeSSR1044 and Embra394) contained alleles of putative genes with known functional importance for response to climatic factors. Our study presents critical information on the population diversity and structure of the important woody species E. grandis and provides insight into the adaptive responses of perennial trees to climatic variations.