It is an open question whether preferences for visual art can be lawfully predicted from the basic constituent elements of a visual image. Here, we developed and tested a computational framework to investigate how aesthetic values are formed. We show that it is possible to explain human preferences for a visual art piece based on a mixture of low- and high-level features of the image. Subjective value ratings could be predicted not only within but also across individuals, using a regression model with a common set of interpretable features. We also show that the features predicting aesthetic preference can emerge hierarchically within a deep convolutional neural network trained only for object recognition. Our findings suggest that human preferences for art can be explained at least in part as a systematic integration over the underlying visual features of an image.