After COVID-19 infection, some patients develop a post-COVID condition (PCC) that is popularly referred to as long COVID. Among its symptoms is persistent cognitive dysfunction that is potentially linked to altered brain functional connectivity (FC). While research has explored functional reorganization in patients with PCC, the intra- and inter- network connectivity and its relationship with cognitive status and clinical outcomes remain unclear. In this study, we recruited 121 individuals with PCC (67 with, and 54 without, cognitive impairment), 20 months after infection, along with 37 non-infected healthy controls from the NAUTILUS Project (ClinicalTrials.gov IDs: NCT05307549 and NCT05307575). Participants underwent resting-state functional magnetic resonance imaging and comprehensive neuropsychological assessment. Resting-state networks were characterized using independent component analyses, dual regression and network modelling for individual FC characterization. Group differences in intra- and inter-network FC, and their associations with clinical and neuropsychological data, were studied. Significance was set at a corrected p-value of < 0.05. Patients with PCC showed increased intra-network FC in 10 cognitively relevant networks, including the default mode, salience, executive control, auditory and basal ganglia networks, correlating positively with general cognition (Montreal Cognitive Assessment scores), time since infection, fatigue and subjective memory failures. Increased inter-network FC between default mode and sensorimotor networks was also observed. Increases in FC may reflect an inefficient compensatory mechanism in patients with PCC, associated with fatigue, subjective memory complaints and persistence of PCC.