The problem of controllability of open quantum systems (i.e., quantum systems interacting with an environment), whose dynamics is described by a non-Markowian master equation is addressed. The manipulations of the dynamics is realized with both a laser eld and a tailored nonequilibrium, and generally time-dependent, state of the surrounding environment. Lie algebra theory is used to characterize the structures of the reachable states sets and to prove controllability. The theoretical results are supported by examples.