Low-frequency 1q21.1 distal deletion and duplication copy number variant (CNV) carriers are predisposed to multiple neurodevelopmental disorders, including schizophrenia, autism and intellectual disability. Human carriers display a high prevalence of micro- and macrocephaly in deletion and duplication carriers, respectively. The underlying brain structural diversity remains largely unknown. We systematically called CNVs in 38 cohorts from the large-scale ENIGMA-CNV collaboration and the UK Biobank and identified 28 1q21.1 distal deletion and 22 duplication carriers and 37,088 non-carriers (48% male) derived from 15 distinct magnetic resonance imaging scanner sites. With standardized methods, we compared subcortical and cortical brain measures (all) and cognitive performance (UK Biobank only) between carrier groups also testing for mediation of brain structure on cognition. We identified positive dosage effects of copy number on intracranial volume (ICV) and total cortical surface area, with the largest effects in frontal and cingulate cortices, and negative dosage effects on caudate and hippocampal volumes. The carriers displayed distinct cognitive deficit profiles in cognitive tasks from the UK Biobank with intermediate decreases in duplication carriers and somewhat larger in deletion carriers—the latter potentially mediated by ICV or cortical surface area. These results shed light on pathobiological mechanisms of neurodevelopmental disorders, by demonstrating gene dose effect on specific brain structures and effect on cognitive function.