A latent measure of white matter microstructure (gWM) provides a neural basis for information processing speed and intelligence in adults, but the temporal emergence of gWM during human development is unknown. We provide evidence that substantial variance in white matter microstructure is shared across a range of major tracts in the newborn brain. Based on diffusion MRI scans from 145 neonates [gestational age (GA) at birth range 23+2–41+5 weeks], the microstructural properties of eight major white matter tracts were calculated using probabilistic neighborhood tractography. Principal component analyses (PCAs) were carried out on the correlations between the eight tracts, separately for four tract-averaged water diffusion parameters: fractional anisotropy, and mean, radial and axial diffusivities. For all four parameters, PCAs revealed a single latent variable that explained around half of the variance across all eight tracts, and all tracts showed positive loadings. We considered the impact of early environment on general microstructural properties, by comparing term-born infants with preterm infants at term equivalent age. We found significant associations between GA at birth and the latent measure for each water diffusion measure; this effect was most apparent in projection and commissural fibers. These data show that a latent measure of white matter microstructure is present in very early life, well before myelination is widespread. Early exposure to extra-uterine life is associated with altered general properties of white matter microstructure, which could explain the high prevalence of cognitive impairment experienced by children born preterm.