Humans can infer the three-dimensional structure of objects from two-dimensional visual inputs. Modeling this ability has been a longstanding goal for the science and engineering of visual intelligence, yet decades of computational methods have fallen short of human performance. Here we develop a modeling framework that predicts human 3D shape inferences for arbitrary objects, directly from experimental stimuli. We achieve this with a novel class of neural networks trained using a visual-spatial objective over naturalistic sensory data; given a set of images taken from different locations within a natural scene, these models learn to predict spatial information related to these images, such as camera location and visual depth, without relying on any object-related inductive biases. Notably, these visual-spatial signals are analogous to sensory cues readily available to humans. We design a zero-shot evaluation approach to determine the performance of these 'multi-view' models on a well established 3D perception task, then compare model and human behavior. Our modeling framework is the first to match human accuracy on 3D shape inferences, even without task-specific training or fine-tuning. Remarkably, independent readouts of model responses predict fine-grained measures of human behavior, including error patterns and reaction times, revealing a natural correspondence between model dynamics and human perception. Taken together, our findings indicate that human-level 3D perception can emerge from a simple, scalable learning objective over naturalistic visual-spatial data. Code, images, and human data needed to reproduce all analyses can be found at https://tzler.github.io/human_multiview/