Abstract Recent experimental works have implicated astrocytes as a significant cell type underlying several neuronal processes in the mammalian brain, from encoding sensory information to neurological disorders. Despite this progress, it is still unclear how astrocytes are communicating with and driving their neuronal neighbors. While previous computational modeling works have helped propose mechanisms responsible for driving these interactions, they have primarily focused on interactions at the synaptic level, with microscale models of calcium dynamics and neurotransmitter diffusion. Since it is computationally infeasible to include the intricate microscale details in a network-scale model, little computational work has been done to understand how astrocytes may be influencing spiking patterns and synchronization of large networks. We overcome this issue by first developing an “effective” astrocyte that can be easily implemented to already established network frameworks. We do this by showing that the astrocyte proximity to a synapse makes synaptic transmission faster, weaker, and less reliable. Thus, our “effective” astrocytes can be incorporated by considering heterogeneous synaptic time constants, which are parametrized only by the degree of astrocytic proximity at that synapse. We then apply our framework to large networks of exponential integrate-and-fire neurons with various spatial structures. Depending on key parameters, such as the number of synapses ensheathed and the strength of this ensheathment, we show that astrocytes can push the network to a synchronous state and exhibit spatially correlated patterns. Author summary In many areas of the brain, glial cells called astrocytes wrap their processes around synapses – the points of contact between neurons. The number of wrapped synapses and the tightness of wrapping varies between brain areas and changes during some diseases, such as epilepsy. We investigate the effect that this synaptic ensheathment has on communication between neurons and the resulting collective dynamics of the neuronal network. We present a general, computationally-efficient way to include astrocytes in neuronal networks using an “effective astrocyte” representation derived from detailed microscopic scale models. The resulting hybrid networks allow us to emulate and observe the effect of ensheathment conditions corresponding to different brain areas and disease states. In particular, we find that it makes the networks more likely to switch into a highly correlated regime, contrary to predictions from the traditional neurons-only view. These results open a new perspective on neural network dynamics, where our understanding of conditions for generating correlated brain activity (e.g., rhythms associated with various brain functions, epileptic seizures) needs to be reevaluated.