This paper establishes global convergence and provides global bounds of the convergence rate of the Heavy-ball method for convex optimization problems. When the objective function has Lipschitz-continuous gradient, we show that the Ces谩ro average of the iterates converges to the optimum at a rate of O(1/k) where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum.