A genetic study of North African populations has revealed a complex migration history from the Middle East, Europe and sub-Saharan Africa. Indigenous Maghrebian heredity and shared heredity with the Middle East, Europe and sub-Saharan Africa were discovered. Migrations from West Africa to Morocco and from Nilotic peoples to Egypt have been dated to about 1200 and 750 years ago. North African populations differ from those of sub-Saharan Africa in terms of cultural, linguistic and phenotypic characteristics: however, the timing and extent of genetic divergence between populations north and south of the Sahara remain poorly understood. Here, we explore the multilayered history of North Africa, characterizing the impact of hypothetical migrations from the Middle East, Europe and sub-Saharan Africa on current genetic diversity. We present dense genome-wide SNP genotyping array data (730,000 sites) from seven North African populations stretching from Egypt to Morocco, and one Spanish population. We identify a gradient of probable autochthonous Maghreb ancestry that increases from east to west across North Africa: this ancestry likely originates from gene flow "back to Africa" more than 12,000 years ago (ya), before the Holocene. Native North African ancestry is more common in populations of historic Berber ethnicity. We also see significant common ancestry with the Middle East in most North African populations, and to a lesser extent with sub-Saharan Africa and Europe. To estimate the timing of the migration of sub-Saharan African populations to North Africa, we implement a maximum likelihood dating method based on the distribution of migration routes. To first identify migration routes, we assign local ancestry to haplotypes using a new analysis based on the principal components of three ancestral populations. We estimate that the migration of people with West African ancestry to Morocco began about 40 generations ago (about 1,200 years ago): the migration of people with Nilotic ancestry to Egypt occurred about 25 generations ago (about 750 years ago). Our genomic data reveal an extremely complex migration history, involving at least five ancestral populations, to North Africa.