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Process variations and device aging impose profound challenges for circuit designers. Without a precise understanding of the impact of variations on the delay of circuit paths, guardbands, which keep timing violations at bay, cannot be correctly estimated. This problem is exacerbated for advanced technology nodes, where transistor dimensions reach atomic levels and established margins are severely constrained. Hence, traditional worst-case analysis becomes impractical, resulting in intolerable performance overheads. Contrarily, process-variation/aging-aware static timing analysis (STA) equips designers with accurate statistical delay distributions. Timing guardbands that are small, yet sufficient, can then be effectively estimated. However, such analysis is costly as it requires intensive Monte-Carlo simulations. Further, it necessitates access to confidential physics-based aging models to generate the standard-cell libraries required for STA. In this work, we employ graph neural networks (GNNs) to accurately estimate the impact of process variations and device aging on the delay of any path within a circuit. Our proposed GNN4REL framework empowers designers to perform rapid and accurate reliability estimations without accessing transistor models, standard-cell libraries, or even STA; these components are all incorporated into the GNN model via training by the foundry. Specifically, GNN4REL is trained on a FinFET technology model that is calibrated against industrial 14nm measurement data. Through our extensive experiments on EPFL and ITC-99 benchmarks, as well as RISC-V processors, we successfully estimate delay degradations of all paths -- notably within seconds -- with a mean absolute error down to 0.01 percentage points.