In this letter, we explore in detail the potential of nanoheteroepitaxy to controllably fabricate high quality GeSn nano-structures and to further improve the crystallinity of GeSn alloys directly grown on Si(001). The GeSn was grown by molecular beam epitaxy at relatively high temperatures up to 750 °C on pre-patterned Si nano-pillars embedded in a SiO2 matrix. The best compromise between selective GeSn growth and homogenous Sn incorporation of 1.4% was achieved at a growth temperature of 600 °C. X-ray diffraction measurements confirmed that our growth approach results in both fully relaxed GeSn nano-islands and negligible Si interdiffusion into the core of the nanostructures. Detailed transmission electron microscopy characterizations show that only the small GeSn/Si interface area reveals defects, such as stacking faults. Importantly, the main part of the GeSn islands is defect-free and of high crystalline quality. The latter was further demonstrated by photoluminescence measurements where a clear redshift of the direct ΓC-ΓV transition was observed with increasing Sn content