Colloidal chemistry, in combination with nanoparticle (NP)/support epitaxial interactions is used here to synthesize shape-selected and thermodynamically stable metallic NPs over a broad range of NP sizes. The morphology of three-dimensional palladium and platinum NPs supported on TiO2(110) was investigated using scanning tunneling microscopy. Well-defined Pd and Pt NPs were synthesized via inverse micelle encapsulation. The initially spherical NPs were found to become faceted and form an epitaxial relationship with the support after high-temperature annealing (e.g., 1100 degrees C). Shape selection was achieved for almost all Pd NPs, namely, a truncated octahedron shape with (111) top and interfacial facets. The Pt NPs were however found to adopt a variety of shapes. The epitaxial relationship of the NPs with the support was evidenced by the alignment of the cluster's edges with TiO2(110)- atomic rows and was found to be responsible for the shape control. The ability of synthesizing thermally stable shape-selected metal NPs demonstrated here is expected to be of relevance for applications in the field of catalysis, since the activity and selectivity of NP catalysts has been shown to strongly depend on the NP shape.