Higher cognitive functioning is supported by adaptive reconfiguration of large-scale functional brain networks. Cognitive control (CC), which plays a vital role in flexibly guiding cognition and behavior in accordance with our goals, supports a range of executive functions via distributed brain networks. These networks process information dynamically and can be represented as functional connectivity changes between network elements. Using graph theory, we explored context-dependent network reorganization in 56 healthy adults performing fMRI tasks from two cognitive domains that varied in CC and episodic-memory demands. We examined whole-brain modular structure during the DPX task, which engages proactive CC in the frontal-parietal cognitive-control network (FPN), and the RiSE task, which manipulates CC demands at encoding and retrieval during episodic-memory processing, and engages FPN, the medial-temporal lobe and other memory-related networks in a context dependent manner. Analyses revealed different levels of network integration and segregation. Modularity analyses revealed greater brain-wide integration across tasks in high CC conditions compared to low CC conditions. Greater network reorganization occurred in the RiSE memory task, which is thought to require coordination across multiple brain networks, than in the DPX cognitive-control task. Finally, FPN, ventral attention, and visual systems showed within network connectivity effects of cognitive control; however, these cognitive systems displayed varying levels of network reorganization. These findings provide insight into how brain networks reorganize to support differing task contexts, suggesting that the FPN flexibly segregates during focused proactive control and integrates to support control in other domains such as episodic memory.