The date of human arrival to the New World has been debated for more than a century. In contrast to the traditional method of careful scrutinization of artifacts, stratigraphy, and dates from individual archaeological sites, we approach the problem using two novel but independent quantitative methods: 1) we use basic principles of human demography, archaeological site formation, and archaeological sampling to simulate the age range of plausible earliest archaeological sites, and 2) time series analysis of a large database of archaeological radiocarbon dates to identify the earliest unequivocal signal of human presence in North America. Both methods indicate a late arrival of humans to the New World south of the ice sheets, between 14,200 and 13,400 BP, with a most likely colonization date falling in the century surrounding 13,800 BP.