Claims of culture in animals have been stimulated by studies on a wide range of taxa revealing group-specific behavior patterns that remain stable through generations, consistent with different behavioral innovations spreading within groups by social transmission in a manner similar to human culture. In chimpanzees, 39 behaviors have been identified as 'cultural', because alternative genetic and environmental explanations for the observed regional variation appear less plausible. This interpretation is supported by experimental data from captive chimpanzee groups. However, there is no experimental evidence for social learning in the wild, nor has there been direct observation of social diffusion of spontaneously occurring behavioral innovations. Here, we document the spread of two novel tool-use variants, 'moss-sponging' and 'leaf-sponge re-use', in the Sonso chimpanzee community of Budongo Forest, Uganda. We use traditional network-based diffusion analysis (NBDA) to test whether these novel behaviors spread by social learning, as well as a newly developed dynamic version of NBDA, capable of capturing temporal aspects of acquisition, i.e. how each successive personal observations impact the subsequent acquisition of behavior. Both models provide strong evidence that diffusion patterns of moss-sponging, but not leaf-sponge re-use, are significantly better explained by social than asocial learning, therefore showing that wild chimpanzees socially learned moss-sponging from each other. The most conservative estimate of social transmission accounts for 85% of observed events with an estimated 11-fold increase in learning rate for each time a novice observed an informed individual performing moss-sponging. We conclude that group-specific behavioral variants in chimpanzees can be socially learned, suggesting this prerequisite for culture originated in a common ancestor of great apes and humans, long before the advent of modern humans.