The theoretical basis of Arrhenius rate law which is the paradigm of thermally activated processes, in general, rests on equilibrium statistical mechanics and more generally on non-equilibrium stochastic processes. Here we present a study of quantum dynamical generalization of the expression for rate coefficient in the context of quantum non-equilibrium processes in condensed media. Brownian motion lies at the heart of activated rate processes and quantum Brownian motion as compared to its classical counterpart rests on a technically different footing. Here we develop a scheme that leads to a natural extension of the classical method to the quantum domain within canonical quantization procedure. It is necessary that such a formalism must be equipped to deal with arbitrary strength of coupling between the system and the reservoir, correlation time of the noise and temperature of the thermal bath. In addition, the scheme must be consistent with macroscopic thermodynamics and quantum-classical correspondence. Here we develop such a scheme for quantum Brownian motion with application to activated rate processes in the various damping regimes, temperatures and noise-correlations.