The adoption of agriculture, first documented ~12,000 years ago in the Fertile Crescent, triggered a rapid shift toward starch-rich diets in human populations. Amylase genes facilitate starch digestion and increased salivary amylase copy number has been observed in some modern human populations with high starch intake, though evidence of recent selection is lacking. Here, using 52 long-read diploid assemblies and short read data from ~5,600 contemporary and ancient humans, we resolve the diversity, evolutionary history, and selective impact of structural variation at the amylase locus. We find that both salivary and pancreatic amylase genes have higher copy numbers in populations with agricultural subsistence compared to fishing, hunting, and pastoral groups. We identify 28 distinct amylase structural architectures and demonstrate that identical structures have arisen independently multiple times throughout recent human history. Using a pangenome graph-based approach to infer structural haplotypes across thousands of humans, we identify extensively duplicated haplotypes present at higher frequencies in modern agricultural populations. Leveraging 534 ancient human genomes we find that duplication-containing haplotypes have increased in frequency more than seven-fold over the last 12,000 years providing evidence for recent selection in Eurasians at this locus comparable in magnitude to that at lactase. Together, our study highlights the strong impact of the agricultural revolution on human genomes and the importance of long-read sequencing in identifying signatures of selection at structurally complex loci.