Homozygosity has long been associated with rare, often devastating, Mendelian disorders, and Darwin was one of the first to recognize that inbreeding reduces evolutionary fitness. However, the effect of the more distant parental relatedness that is common in modern human populations is less well understood. Genomic data now allow us to investigate the effects of homozygosity on traits of public health importance by observing contiguous homozygous segments (runs of homozygosity), which are inferred to be homozygous along their complete length. Given the low levels of genome-wide homozygosity prevalent in most human populations, information is required on very large numbers of people to provide sufficient power. Here we use runs of homozygosity to study 16 health-related quantitative traits in 354,224 individuals from 102 cohorts, and find statistically significant associations between summed runs of homozygosity and four complex traits: height, forced expiratory lung volume in one second, general cognitive ability and educational attainment (P < 1 x 10-300, 2.1 x 10-6, 2.5 x 10-10 and 1.8 x 10-10, respectively). In each case, increased homozygosity was associated with decreased trait value, equivalent to the offspring of first cousins being 1.2 cm shorter and having 10 months' less education. Similar effect sizes were found across four continental groups and populations with different degrees of genome-wide homozygosity, providing evidence that homozygosity, rather than confounding, directly contributes to phenotypic variance. Contrary to earlier reports in substantially smaller samples, no evidence was seen of an influence of genome-wide homozygosity on blood pressure and low density lipoprotein cholesterol, or ten other cardio-metabolic traits. Since directional dominance is predicted for traits under directional evolutionary selection, this study provides evidence that increased stature and cognitive function have been positively selected in human evolution, whereas many important risk factors for late-onset complex diseases may not have been.