Atomically controlled InGaAs/InP quantum well (QW) structures are grown on (001) InP substrates at 350 degrees C by gas source migration-enhanced epitaxy. Raman scattering measurement suggests the formation of tailored heterointerfaces: QWs having only InAs-type interfaces show the absence of Ga-P bonds, while QWs having InGaP-type interfaces indeed show the presence of Ga-P bonds. 4.2 K photoluminescence (PL) spectra for InGaAs/InP QWs show the very narrow line width comparable to the narrowest line width reported so far. PL peak energy variation with well thickness clearly depends on the heterointerface type, suggesting that the potential shifts to higher energies at the InGaP interfaces, while it drops at the InAs interfaces. Theoretical calculations assuming the formation of controlled heterointerfaces reproduce the experimentally observed PL energy variation.