Human herpes simplex virus 1 (HSV-1), a lifelong infection spread by oral contact, infects a majority of adults globally. Phylogeographic clustering of sampled diversity into European, pan-Eurasian, and African groups has suggested the virus codiverged with human migrations out of Africa, although a much younger origin has also been proposed. We present three full ancient European HSV-1 genomes and one partial genome, dating to the 3rd-17th century CE, sequenced to up to 9.5× with paired human genomes up to 10.16×. Considering a dataset of modern and ancient genomes we apply phylogenetic methods to estimate the age of sampled modern Eurasian HSV-1 diversity to 4.68 (3.87 - 5.65) kya. Extrapolation of estimated rates to a global dataset points to the age of extant sampled HSV-1 as 5.29 (4.60-6.12) kya, suggesting HSV-1 lineage replacement coinciding with the late Neolithic period and following Bronze Age migrations.