Many artificial neural networks (ANNs) trained with ecologically plausible objectives on naturalistic data align with behavior and neural representations in biological systems. Here, we show that this alignment is a consequence of convergence onto the same representations by high-performing ANNs and by brains. We developed a method to identify stimuli that systematically vary the degree of inter-model representation agreement. Across language and vision, we then showed that stimuli from high- and low-agreement sets predictably modulated model-to-brain alignment. We also examined which stimulus features distinguish high- from low-agreement sentences and images. Our results establish representation universality as a core component in the model-to-brain alignment and provide a new approach for using ANNs to uncover the structure of biological representations and computations.