Attention facilitates the processing of task-relevant visual information and suppresses interference from task-irrelevant information. Modulations of neural activity in visual cortex depend on attention, and likely result from signals originating in fronto-parietal and cingulo-opercular regions of cortex. Here, we tested the hypothesis that attentional facilitation of visual processing is accomplished in part by changes in how brain networks involved in attentional control interact with sectors of V1 that represent different retinal eccentricities. We measured the strength of background connectivity between frontoparietal and cingulo-opercular regions with different eccentricity sectors in V1 using functional MRI data that were collected while participants performed tasks involving attention to either a centrally presented visual stimulus or a simultaneously presented auditory stimulus. We found that when the visual stimulus was attended, background connectivity between V1 and the left frontal eye fields (FEF), left intraparietal sulcus (IPS), and right IPS varied strongly across different eccentricity sectors in V1 so that foveal sectors were more strongly connected than peripheral sectors. This retinotopic gradient was weaker when the visual stimulus was ignored, indicating that it was driven by attentional effects. Greater task-driven differences between foveal and peripheral sectors in background connectivity to these regions were associated with better performance on the visual task and faster response times on correct trials. These findings are consistent with the notion that attention drives the configuration of task-specific functional pathways that enable the prioritized processing of task-relevant visual information, and show that the prioritization of visual information by attentional processes may be encoded in the retinotopic gradient of connectivty between V1 and fronto-parietal regions.