Populations change in size over time due to factors such as population growth, migration, bottleneck events, natural disasters, and disease. The historical effective size of a population affects the power and resolution of genetic association studies. For admixed populations, it is not only the overall effective population size that is of interest, but also the effective sizes of the component ancestral populations. We use identity by descent and local ancestry inferred from genome-wide genetic data to estimate overall and ancestry-specific effective population size during the past hundred generations for nine admixed American populations from the Hispanic Community Health Study/Study of Latinos, and for African-American and European-American populations from two US cities. In these populations, the estimated pre-admixture effective sizes of the ancestral populations vary by sampled population, suggesting that the ancestors of different sampled populations were drawn from different sub-populations. In addition, we estimate that overall effective population sizes dropped substantially in the generations immediately after the commencement of European and African immigration, reaching a minimum around 12 generations ago, but rebounded within a small number of generations afterwards. Of the populations that we considered, the population of individuals originating from Puerto Rico has the smallest bottleneck size of one thousand, while the Pittsburgh African-American population has the largest bottleneck size of two hundred thousand.