A smooth manifold M n {M^n} is called integrably parallelizable if there exists an atlas for the smooth structure on M n {M^n} such that all differentials in overlap between charts are equal to the identity map of the model for M n {M^n} . We show that the class of connected, integrably parallelizable, n -dimensional smooth manifolds consists precisely of the open parallelizable manifolds and manifolds diffeomorphic to the n -torus.