The Kondo effect observed for surface magnetic impurities is successfully controlled using magnetic metal multilayers. Low-temperature scanning tunneling spectroscopy of Co adatoms on Cu/Co/Cu(100) multilayers reveals the Kondo resonance, whose analysis based on the Fano line shape gives the Kondo temperatures T_K. T_K varies between 60 K and 157 K as the Cu overlayer thickness changes from 20 to 5 atomic layers. This is attributed to the modulation of the density of states at the Fermi level due to formation of quantum well states in the Cu overlayer.