The structure of the human brain changes in several ways throughout childhood and adolescence. Perhaps the most salient of these changes is the strengthening of white matter tracts that enable distal brain regions to communicate with one another more quickly and efficiently. Here, we sought to understand whether and how white matter changes contribute to improved reasoning ability over development. In particular, we sought to understand whether previously reported relationships between white matter microstructure and reasoning are mediated by processing speed. To this end, we analyzed diffusion tensor imaging data as well as data from standard psychometric tests of cognitive abilities from 103 individuals between the ages of 6 and 18. We used structural equation modeling to investigate the network of relationships between brain and behavior variables. Our analyses provide support for the hypothesis that white matter maturation (as indexed either by microstructural organization or volume) supports improved processing speed, which, in turn, supports improved reasoning ability.