Pleiotropy occurs when a genetic variant influences more than one trait. This is a key property of the genomic architecture of psychiatric disorders and has been observed for rare and common genomic variants. It is reasonable to hypothesize that the microscale genetic overlap (pleiotropy) across psychiatric conditions and cognitive traits may lead to similar overlaps at the macroscale brain level such as large-scale brain functional networks. We took advantage of brain connectivity, measured by resting-state functional MRI to measure the effects of pleiotropy on large-scale brain networks, a putative step from genes to behaviour. We processed nine resting-state functional MRI datasets including 32 726 individuals and computed connectome-wide profiles of seven neuropsychiatric copy-number-variants, five polygenic scores, neuroticism and fluid intelligence as well as four idiopathic psychiatric conditions. Nine out of 19 pairs of conditions and traits showed significant functional connectivity correlations (rFunctional connectivity), which could be explained by previously published levels of genomic (rGenetic) and transcriptomic (rTranscriptomic) correlations with moderate to high concordance: rGenetic-rFunctional connectivity = 0.71 [0.40-0.87] and rTranscriptomic-rFunctional connectivity = 0.83 [0.52; 0.94]. Extending this analysis to functional connectivity profiles associated with rare and common genetic risk showed that 30 out of 136 pairs of connectivity profiles were correlated above chance. These similarities between genetic risks and psychiatric disorders at the connectivity level were mainly driven by the overconnectivity of the thalamus and the somatomotor networks. Our findings suggest a substantial genetic component for shared connectivity profiles across conditions and traits, opening avenues to delineate general mechanisms-amenable to intervention-across psychiatric conditions and genetic risks.