The superconducting phase diagrams have been established by the measurements of electrical resistivity, magnetic susceptibility, and thermopower in cobalt-doped LFeAsO (L=La and Sm) systems. It is shown that the antiferromagnetic spin-density-wave order in the parent compounds is rapidly suppressed by Co doping, and superconductivity emerges at x=0.025 and 0.05 in LaFe1−xCoxAsO and SmFe1−xCoxAsO, respectively. The Tc(x) curves of both systems are domelike, with a maximum Tc of 13 K at x=0.075 in LaFe1−xCoxAsO and 17.2 K at x=0.1 in SmFe1−xCoxAsO. Thermopower measurement shows dominant electron-type transport for the Co-doped samples, in accordance with itinerant character of Co 3d electrons. We found a close correlation between Tc and the abnormally enhanced part of normal-state thermopower. The occurrence of superconductivity via the Fe-site doping in the iron-based oxyarsenide contrasts sharply with the destruction of superconductivity by the Cu-site (within CuO2 planes) doping in high-temperature superconducting cuprates.