We investigate the structural properties and strain state of Ge nano-structures selectively grown on Si pillars of about 60 nm diameter with different SiGe buffer layers. A matrix of TEOS SiO2 surrounding the Si nano-pillars causes a tensile strain in the top part at the growth temperature of the buffer that reduces the misfit and supports defect-free initial growth. Elastic relaxation plays the dominant role in the further increase of the buffer thickness and subsequent Ge deposition. This method leads to Ge nanostructures on Si that are free from misfit dislocations and other structural defects, which is not the case for direct Ge deposition on these pillar structures. The Ge content of the SiGe buffer is thereby not a critical parameter; it may vary over a relatively wide range.