Altered structural fetal brain development has been linked to neuro-developmental disorders. These structural alterations can be potentially detected in utero using diffusion tensor imaging (DTI). However, acquisition and reconstruction of in utero fetal brain DTI remains challenging. Until now, motion-robust DTI methods have been employed for reconstruction of in utero fetal DTIs. However, due to the unconstrained fetal motion and permissible in utero acquisition times, these methods yielded limited success and have typically resulted in noisy DTIs. Consequently, atlases and methods that could enable groupwise studies, multi-modality imaging, and computer-aided diagnosis from in utero DTIs have not yet been developed. This paper presents the first DTI atlas of the fetal brain computed from in utero diffusion-weighted images. For this purpose an algorithm for computing an unbiased spatiotemporal DTI atlas, which integrates kernel-regression in age with a diffeomorphic tensor-to-tensor registration of motion-corrected and reconstructed individual fetal brain DTIs, was developed. Our new algorithm was applied to a set of 67 fetal DTI scans acquired from healthy fetuses each scanned at a gestational age between 21 and 39 weeks. The neurodevelopmental trends in the fetal brain, characterized by the atlas, were qualitatively and quantitatively compared with the observations reported in prior ex vivo and in utero studies, and with results from imaging gestational-age equivalent preterm infants. Our major findings revealed early presence of limbic fiber bundles, followed by the appearance and maturation of projection pathways (characterized by an age related increase in FA) during late 2nd and early 3rd trimesters. During the 3rd trimester association fiber bundles become evident. In parallel with the appearance and maturation of fiber bundles, from 21 to 39 gestational weeks gradual disappearance of the radial coherence of the telencephalic wall was qualitatively identified. These results and analyses show that our DTI atlas of the fetal brain is useful for reliable detection of major neuronal fiber bundle pathways and for characterization of the fetal brain reorganization that occurs in utero. The atlas can also serve as a useful resource for detection of normal and abnormal fetal brain development in utero.