The Mpemba effect, where a far-from-equilibrium state relaxes faster than a state closer to equilibrium, has been extensively studied in classical systems and recently in quantum systems. However, the relationship between this effect and memory in quantum systems remains unexplored. This work investigates non-Markovian open quantum systems and reveals new classes of quantum Mpemba effects, which do not exist in Markovian quantum dynamics. In these systems, the dynamics are characterized by a finite memory time and a unique steady state. Even if the system is initialized in the steady state, it can take a long time to relax back. The authors find initial states that reach the steady state much faster, and demonstrate that there can be an initial state where the system reaches the steady state within the finite memory time, achieving the fastest possible relaxation to stationarity. The effect is verified through numerical calculations for quantum dot systems coupled to electronic reservoirs in equilibrium and non-equilibrium setups at weak, intermediate, and strong coupling, with and without interactions. The findings provide new insights into the physics underlying accelerated relaxation in quantum systems.The Mpemba effect, where a far-from-equilibrium state relaxes faster than a state closer to equilibrium, has been extensively studied in classical systems and recently in quantum systems. However, the relationship between this effect and memory in quantum systems remains unexplored. This work investigates non-Markovian open quantum systems and reveals new classes of quantum Mpemba effects, which do not exist in Markovian quantum dynamics. In these systems, the dynamics are characterized by a finite memory time and a unique steady state. Even if the system is initialized in the steady state, it can take a long time to relax back. The authors find initial states that reach the steady state much faster, and demonstrate that there can be an initial state where the system reaches the steady state within the finite memory time, achieving the fastest possible relaxation to stationarity. The effect is verified through numerical calculations for quantum dot systems coupled to electronic reservoirs in equilibrium and non-equilibrium setups at weak, intermediate, and strong coupling, with and without interactions. The findings provide new insights into the physics underlying accelerated relaxation in quantum systems.