Effective connectivity (EC), indicative of the causal interactions between brain regions, is fundamental to understanding information processing in the brain. Traditional approaches, which infer EC from neural responses to stimulations, are not suited for mapping whole-brain EC in human due to being invasive and limited spatial coverage of stimulations. To address this gap, we present Neural Perturbational Inference (NPI), a data-driven framework designed to map EC across the entire brain. NPI employs an artificial neural network trained to learn large-scale neural dynamics as a computational surrogate of the brain. NPI maps EC by perturbing each region of the surrogate brain and observing the resulting responses in the rest of regions. NPI captures the directionality, strength, and excitatory/inhibitory properties of EC on a brain-wide scale. Our validation of NPI, using models with established EC, shows its superiority over Granger Causality and Dynamic Causal Modeling. Applying NPI to resting-state fMRI data from diverse datasets reveals consistent and structurally supported EC. Applications on a disease-specific dataset highlight the potential of using personalized EC as biomarkers for neurological diseases. By transitioning from correlational to causal understandings of brain functionality, NPI marks a stride in decoding the brain's functional architecture and can facilitate neuroscience research and clinical applications.