Healthy aging is associated with structural and functional changes in the brain even in individuals who are free of neurodegenerative diseases. Using resting state functional magnetic resonance imaging data from a carefully selected cohort of participants, we examined cross sectional changes in the functional organization of several large-scale brain networks over the adult lifespan and its potential association with general cognitive performance. Converging results from multiple analyses at the voxel, node, and network levels showed widespread reorganization of functional brain networks with increasing age. Specifically, the primary processing (visual and sensorimotor) and visuospatial (dorsal attention) networks showed diminished network integrity, while the so-called core neurocognitive (executive control, salience, and default mode) and basal ganglia networks exhibited relatively preserved between-network connections. The visuospatial and precuneus networks also showed significantly more widespread increased connectivity with other networks. Graph analysis suggested that this reorganization progressed towards a more integrated network topology. General cognitive performance, assessed by Addenbrooke's Cognitive Examination-Revised total score, was positively correlated with between-network connectivity among the core neurocognitive and basal ganglia networks and the integrity of the primary processing and visuospatial networks. Mediation analyses further indicated that the observed association between aging and relative decline in cognitive performance could be mediated by changes in relevant functional connectivity measures. Overall, these findings provided further evidence supporting widespread age-related brain network reorganization and its potential association with general cognitive performance during healthy aging.