The Faroe Islands are home to descendants of a North Atlantic founder population with a unique history shaped by both migration and periods of relative isolation. Here, we investigate the genetic diversity, population structure, and demographic history of the islands by analyzing whole genome sequencing data from 40 participants in the Faroe Genome Project. This represents the first whole genome sequencing panel of this size from the Faroe Islands. We observed numerous putatively functional private alleles, including stop gain variants and high impact missense variants in the cohort. Faroese individuals had a higher proportion of their genomes contained in long runs of homozygosity than other European groups, including Finnish, suggesting a more recent or stronger bottleneck in the Faroese population. Signals of positive selection were identified at loci containing genes that play roles in vitamin D and dietary fat absorption and DNA repair, while increased diversity on lactase persist