Schizophrenia (SZ) and bipolar disorder (BD) share clinical features, genetic risk factors and neuroimaging abnormalities. There is evidence of disrupted connectivity in resting state networks in patients with SZ and BD and their unaffected relatives. Resting state networks are known to undergo reorganization during youth coinciding with the period of increased incidence for both disorders. We therefore focused on characterizing resting state network connectivity in youth at familial risk for SZ or BD to identify alterations arising during this period. We measured resting-state functional connectivity in a sample of 106 youth, aged 7-19 years, comprising offspring of patients with SZ (N = 27), offspring of patients with BD (N = 39) and offspring of community control parents (N = 40). We used Independent Component Analysis to assess functional connectivity within the default mode, executive control, salience and basal ganglia networks and define their relationship to grey matter volume, clinical and cognitive measures. There was no difference in connectivity within any of the networks examined between offspring of patients with BD and offspring of community controls. In contrast, offspring of patients with SZ showed reduced connectivity within the left basal ganglia network compared to control offspring, and they showed a positive correlation between connectivity in this network and grey matter volume in the left caudate. Our findings suggest that dysconnectivity in the basal ganglia network is a robust correlate of familial risk for SZ and can be detected during childhood and adolescence.