This paper addresses the problem of global well-posedness of a coupled system of Korteweg-de Vries equations, derived by Majda and Biello in the context of nonlinear resonant interaction of Rossby waves, in a periodic setting in homogeneous Sobolev spaces H˙^s, for s ≥0. Our approach is based on a successive time-averaging method developed by Babin, Ilyin and Titi [A.V. Babin, A.A. Ilyin and E.S. Titi, Commun. Pure Appl. Math., 64(5), 591-648, 2011].