The melanoma genome is dominated by ultraviolet radiation (UVR)-induced mutations. Their relevance in disease progression is unknown. Here we classify melanomas by mutation signatures and identify ten recurrently mutated UVR signature genes that predict patient survival. We validate these findings in primary human melanomas; in mice we show that this signature is imprinted by short-wavelength UVR and that four exposures to UVR are sufficient to accelerate melanomagenesis.