The Blue Brain Project endeavors to reconstruct and simulate the rodent brain at various scales: from single-neuron gene expression profiles and membrane permeabilities to large-scale neuronal circuits. One important aspect is the biologically accurate morphological structure of neurons, as morphology constrains the connectivity and impacts the functionality of brain networks. Biologically realistic dendrites within brain regions could be successfully synthesized using topological neuron synthesis (TNS), but inter-regional connectivity remains largely an open question which we address in this work, focusing on long-range axon synthesis.Dendrites tend to grow isotropically, whereas axons target specific brain regions, which is why they require a different synthesis algorithm. We first use unsupervised clustering with Gaussian Mixture Models (GMMs) trained on open morphologies databases (NeuroMorpho, MouseLight), to define axonal-projection classes for each source brain region. The axon trunk is then synthesized using a Prize Collecting Steiner Tree (PCST) algorithm, which minimizes the trunk length while connecting target points and satisfying biological constraints. Finally, we grow tufts from the trunk inside the target regions using the TNS algorithm.We validated the GMM clustering, showing for instance that it recovers the same projection classes as previously reported for the presubiculum using hierarchical clustering on the MouseLight dataset. The axon trunk morphometrics are in statistical agreement with biological axons. Assuming the training dataset is representative of the biological connectome, we demonstrate that structural connectivity is accurately reproduced. However, our methodology is designed to generalize on new connectivity datasets and synthesize the axons accordingly.