Across networks, connectivity within the frontoparietal network (FPN) and cingulo-opercular network (CON) exhibits reductions earliest during healthy aging, contributing to cognitive impairment. Individuals with psychotic disorders demonstrate evidence of accelerated aging across multiple biological systems. By leveraging a large sample of patients with psychosis from early to chronic illness stages, this study sought to determine whether the CON and FPN exhibit evidence of accelerated aging in psychotic disorders, confirm associations between network efficiency and cognition, and determine whether reduced network efficiency is observed in early-stage psychosis. Resting-state functional magnetic resonance imaging and cognitive data were obtained on 240 patients with psychotic disorder and 178 healthy control participants (HCs). Global efficiency, a measure of functional integration, was calculated for the CON, FPN, subcortical network, and visual network. Associations with age and cognition were assessed and compared between groups. Consistent with accelerated aging, significant group by age interactions reflected significantly stronger relationships between efficiency and age in patients with psychosis than in HCs for both the CON (psychosis: r = −.37; HC: r = −.16) and FPN (psychosis: r = −.31; HC: r = −.05). Accelerated aging was not observed in either the subcortical or visual network, suggesting specificity for cognitive networks that decline earliest in healthy aging. Replicating prior findings, efficiency of both the CON and FPN correlated with cognitive function across all participants (rs > .11, ps < .031). Furthermore, patients with chronic psychosis (p = .004), but not patients with early psychosis (p = .553), exhibited significantly lower FPN efficiency compared with HCs. Functional integration of higher-order cognitive networks is intact in early psychosis but exhibits evidence of accelerated aging, suggesting the potential for intervention targeting cognition within the early psychosis period.