A family history (FH+) of substance use disorder (SUD) increases an adolescent's risk for substance use initiation and progression. Greater impulsivity and reward seeking behavior is known to be associated with such risk. At the neurological level, dysfunction of cortico-striatal and cortico-limbic pathways have been proposed as contributors to the increased SUD risk in adolescents with FH+. In addition, disadvantaged environments have been associated with atypical brain connectivity and higher SUD risk. However, it remains unclear if this increased risk is manifested in structural and functional brain abnormalities prior to regular drug use. To examine this, we employed complementary imaging of structural and functional connectivity of 60 FH+ and 55 FH- minority adolescents, all from families with low socio-economic status. We acquired diffusion tensor-imaging (DTI) and resting state fMRI data across the whole brain. Structural connectivity was examined by measuring fractional anisotropy (FA) using DTI, to indicate integrity of the white matter tracts. Functional connectivity within and between resting state networks was assessed by the correlation of blood-oxygen-level-dependent (BOLD) signal between intra and inter-network nodes. Psychological measures of impulsivity and reward seeking were also obtained with standardized measures, the BIS-11 and the BIS/BAS, and their association with FA and functional connectivity was evaluated. We found no differences in white matter integrity between the groups. Compared to FH-, FH + adolescents showed significantly greater functional connectivity between posterior regions of the Default Mode Network (DMN) and the Fronto-Parietal Network (FPN). While psychological measures of reward seeking behavior did not differ between the FH+ and FH- groups, impulsivity, assessed by the BIS-11, was significantly higher for FH+. However, we did not find significant differences between the FH+ and FH- groups when comparing associations of BIS-11 scores and white matter integrity or functional connectivity measures. The stronger inter-network functional connectivity between the DMN and FPN in FH + adolescents suggests that transmitted risk for SUD may be related to large-scale brain dynamics. The lack of structural differences support the importance of early prevention efforts for FH + adolescents, before initiation of drug use, allowing for healthy brain development.