The highly polygenic and pleiotropic nature of behavioural traits, psychiatric disorders and structural and functional brain phenotypes complicate mechanistic interpretation of related genome-wide association study (GWAS) signals, thereby obscuring underlying causal biological processes. We propose genomic principal and independent component analysis (PCA, ICA) to decompose a large set of univariate GWAS statistics of multimodal brain traits into more interpretable latent genomic components. Here we introduce and evaluate this novel methods various analytic parameters and reproducibility across independent samples. Two UK Biobank GWAS summary statistic releases of 2240 imaging-derived phenotypes (IDPs) were retrieved. Genome-wide beta-values and their corresponding standard-error scaled z-values were decomposed using genomic PCA/ICA. We evaluated variance explained at multiple dimensions up to 200. We tested the inter-sample reproducibility of output of dimensions 5, 10, 25 and 50. Reproducibility statistics of the respective univariate GWAS served as benchmarks. Reproducibility of 10-dimensional PCs and ICs showed the best trade-off between model complexity and robustness and variance explained (PCs: |rz − max| = 0.33, |rraw − max| = 0.30; ICs: |rz − max| = 0.23, |rraw − max| = 0.19). Genomic PC and IC reproducibility improved substantially relative to mean univariate GWAS reproducibility up to dimension 10. Genomic components clustered along neuroimaging modalities. Our results indicate that genomic PCA and ICA decompose genetic effects on IDPs from GWAS statistics with high reproducibility by taking advantage of the inherent pleiotropic patterns. These findings encourage further applications of genomic PCA and ICA as fully data-driven methods to effectively reduce the dimensionality, enhance the signal to noise ratio and improve interpretability of high-dimensional multitrait genome-wide analyses.