1H MRI maps brain structure and function non-invasively through versatile contrasts that exploit inhomogeneity in tissue micro-environments. Inferring histopathological information from magnetic resonance imaging (MRI) findings, however, remains challenging due to absence of direct links between MRI signals and cellular structures. Here, we show that deep convolutional neural networks, developed using co-registered multi-contrast MRI and histological data of the mouse brain, can estimate histological staining intensity directly from MRI signals at each voxel. The results provide three-dimensional maps of axons and myelin with tissue contrasts that closely mimic target histology and enhanced sensitivity and specificity compared to conventional MRI markers. Furthermore, the relative contribution of each MRI contrast within the networks can be used to optimize multi-contrast MRI acquisition. We anticipate our method to be a starting point for translation of MRI results into easy-to-understand virtual histology for neurobiologists and provide resources for validating novel MRI techniques.