Human brain structure changes throughout the lifespan. Altered brain growth or rates of decline are implicated in a vast range of psychiatric, developmental and neurodegenerative diseases. In this study, we identified common genetic variants that affect rates of brain growth or atrophy in what is, to our knowledge, the first genome-wide association meta-analysis of changes in brain morphology across the lifespan. Longitudinal magnetic resonance imaging data from 15,640 individuals were used to compute rates of change for 15 brain structures. The most robustly identified genes GPR139, DACH1 and APOE are associated with metabolic processes. We demonstrate global genetic overlap with depression, schizophrenia, cognitive functioning, insomnia, height, body mass index and smoking. Gene set findings implicate both early brain development and neurodegenerative processes in the rates of brain changes. Identifying variants involved in structural brain changes may help to determine biological pathways underlying optimal and dysfunctional brain development and aging.