The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.