The degree to which genetic factors influence brain connectivity is beginning to be understood. Large-scale efforts are underway to map the profile of genetic effects in various brain regions. The NIH-funded Human Connectome Project (HCP) is providing data valuable for analyzing the degree of genetic influence underlying brain connectivity revealed by state-of-the-art neuroimaging methods. We calculated the heritability of the fractional anisotropy (FA) measure derived from diffusion tensor imaging (DTI) reconstruction in 481 HCP subjects (194/287 M/F) consisting of 57/60 pairs of mono- and dizygotic twins, and 246 siblings. FA measurements were derived using (Enhancing NeuroImaging Genetics through Meta-Analysis) ENIGMA DTI protocols and heritability estimates were calculated using the SOLAR-Eclipse imaging genetic analysis package. We compared heritability estimates derived from HCP data to those publicly available through the ENIGMA-DTI consortium, which were pooled together from five-family based studies across the US, Europe, and Australia. FA measurements from the HCP cohort for eleven major white matter tracts were highly heritable (h2=0.53-0.90, p<10-5), and were significantly correlated with the joint-analytical estimates from the ENIGMA cohort on the tract and voxel-wise levels. The similarity in regional heritability suggests that the additive genetic contribution to white matter microstructure is consistent across populations and imaging acquisition parameters. It also suggests that the overarching genetic influence provides an opportunity to define a common genetic search space for future gene-discovery studies. Uniquely, the measurements of additive genetic contribution performed in this study can be repeated using online genetic analysis tools provided by the HCP ConnectomeDB web application.