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Finland provides unique opportunities to investigate population and medical genomics because of its adoption of unified national electronic health records, detailed historical and birth records, and serial population bottlenecks. We assembled a comprehensive view of recent population history (≤100 generations), the timespan during which most rare-disease-causing alleles arose, by comparing pairwise haplotype sharing from 43,254 Finns to that of 16,060 Swedes, Estonians, Russians, and Hungarians from geographically and linguistically adjacent countries with different population histories. We find much more extensive sharing in Finns, with at least one ≥ 5 cM tract on average between pairs of unrelated individuals. By coupling haplotype sharing with fine-scale birth records from more than 25,000 individuals, we find that although haplotype sharing broadly decays with geographical distance, there are pockets of excess haplotype sharing; individuals from northeast Finland typically share several-fold more of their genome in identity-by-descent segments than individuals from southwest regions. We estimate recent effective population-size changes through time across regions of Finland, and we find that there was more continuous gene flow as Finns migrated from southwest to northeast between the early- and late-settlement regions than was dichotomously described previously. Lastly, we show that haplotype sharing is locally enriched by an order of magnitude among pairs of individuals sharing rare alleles and especially among pairs sharing rare disease-causing variants. Our work provides a general framework for using haplotype sharing to reconstruct an integrative view of recent population history and gain insight into the evolutionary origins of rare variants contributing to disease. [ABSTRACT FROM AUTHOR]