We demonstrate catalyst-free growth of GaAs nanowires by selective-area metal-organic chemical vapor deposition (MOCVD) on GaAs and silicon substrates using a triethylgallium (TEGa) precursor. Two-temperature growth of GaAs nanowires-nucleation at low temperature followed by nanowire elongation at high temperature-almost completely suppresses the radial overgrowth of nanowires on GaAs substrates while exhibiting a vertical growth yield of almost 100%. A 100% growth yield is also achieved on silicon substrates by terminating Si(111) surfaces by arsenic prior to the nanowire growth and optimizing the growth temperature. Compared with trimethylgallium (TMGa) which has been exclusively employed in the vapor-solid phase growth of GaAs nanowires by MOCVD, the proposed growth technique using TEGa is advantageous because of lower growth temperature and fully suppressed radial overgrowth. It is also known that GaAs grown by TEGa induce less impurity incorporation compared with TMGa, and therefore the proposed method could be a building block for GaAs nanowire-based high-performance optoelectronic and nanoelectronic devices on both III-V and silicon platforms.