Long-range axons are fundamental to brain connectivity and functional organization, enabling communication between different brain regions. Recent advances in experimental techniques have yielded a substantial number of whole-brain axonal reconstructions. While previous computational generative models of neurons have predominantly focused on dendrites, generating realistic axonal morphologies is more challenging due to their distinct targeting. In this study, we present a novel algorithm for axon synthesis that combines algebraic topology with the Steiner tree algorithm, an extension of the minimum spanning tree, to generate both the local and long-range compartments of axons. We demonstrate that our computationally generated axons closely replicate experimental data in terms of their morphological properties. This approach enables the generation of biologically accurate long-range axons that span large distances and connect multiple brain regions, advancing the digital reconstruction of the brain. Ultimately, our approach opens up new possibilities for large-scale in-silico simulations, advancing research into brain function and disorders.