Cancer prognostication is a challenging task in computational pathology that requires context-aware representations of histology features to adequately infer patient survival. Despite the advancements made in weakly-supervised deep learning, many approaches are not context-aware and are unable to model important morphological feature interactions between cell identities and tissue types that are prognostic for patient survival. In this work, we present Patch-GCN, a context-aware, spatially-resolved patch-based graph convolutional network that hierarchically aggregates instance-level histology features to model local- and global-level topological structures in the tumor microenvironment. We validate Patch-GCN with 4,370 gigapixel WSIs across five different cancer types from the Cancer Genome Atlas (TCGA), and demonstrate that Patch-GCN outperforms all prior weakly-supervised approaches by 3.58-9.46%. Our code and corresponding models are publicly available at https://github.com/mahmoodlab/Patch-GCN.