Goats play an important role in the livestock sector in Greece. The national herd consists mainly of two indigenous breeds, the Eghoria and Skopelos. Here, we report the population structure and genomic profiles of these two native goat breeds using Illumina's Goat SNP50 BeadChip. Moreover, we present a panel of candidate markers acquired using different genetic models for breed discrimination. Quality control on the initial dataset resulted in 48,841 SNPs kept for downstream analysis. Principal component and admixture analyses were applied to assess population structure. The rate of inbreeding within breed was evaluated based on the distribution of runs of homozygosity in the genome and respective coefficients, the genomic relationship matrix, the patterns of linkage disequilibrium, and the historic effective population size. Results showed that both breeds exhibit high levels of genetic diversity. Level of inbreeding between the two breeds estimated by the Wright's fixation index FST was low (Fst = 0.04362), indicating the existence of a weak genetic differentiation between them. In addition, grouping of farms according to their geographical locations was observed. This study presents for the first time a genome-based analysis on the genetic structure of the two indigenous Greek goat breeds and identifies markers that can be potentially exploited in future selective breeding programs for traceability purposes, targeted genetic improvement schemes and conservation strategies.