Cellular networks in developing regions rely heavily on diesel for energy to provide network coverage due to the paucity of reliable grid power which directly impacts the economic viability of the network and long-term sustainability while also leaving a massive carbon footprint. In this paper, we propose the design, implementation, deployment and evaluation of GreenLinks, an intermittency-aware green cellular network architecture that provides a virtual cell abstraction to extend cellular coverage to areas with unreliable power in a sustainable manner with minimal carbon footprint. GreenLinks relies on a combination of grid-solar powered software-defined cellular routers that can provide a wide range of services including calls, messaging services and mobile web using an intermittency-aware naming, addressing and routing layer that can provide high availability in the face of network failures and partitions. GreenLinks uses an energy-aware routing layer together with its energy monitoring module to perform advance detection and early repair of routes affected by power availability related failures. We demonstrate the effectiveness of GreenLinks using a combination of a small real-world outdoor deployment, an indoor multi-radio deployment and larger-scale evaluation in an emulation environment. Using an economic framework coupled with operational data from a large cellular provider, we show that GreenLinks, in comparison to traditional cellular networks, can provide high reliability and availability while simultaneously providing a substantial reduction in economic costs.