With the widespread integration of renewable energy into distribution networks, energy storage systems are playing an increasingly critical role in maintaining grid stability and sustainability. Hydrogen, as a key zero-carbon energy carrier, offers unique advantages in the transition to low-carbon energy systems. To facilitate the coordination between hydrogen and renewables, this paper proposes a flexible on-grid and off-grid control method for an electric–hydrogen hybrid AC-DC microgrid which integrates photovoltaic panels, battery energy storage, electrolysers, a hydrogen storage tank, and fuel cells. The flexible control method proposed here employs a hierarchical structure. The upper level adopts a power management strategy (PMS) that allocates power to each component based on the states of energy storage. The lower level utilises the master–slave control where master and slave converters are regulated by virtual synchronous generator (VSG) and active and reactive power (PQ) control, respectively. In addition, a pre-synchronisation control strategy which does not rely on traditional phase-locked loops is introduced to enable a smooth transition from the off-grid to on-grid mode. The electric–hydrogen microgrid along with the proposed control method is modelled and tested under various operating modes and scenarios. The simulation results demonstrate that the proposed control method achieves an effective power dispatch within microgrid and maintains microgrid stability in on- and off-grid modes as well as in the transition between the two modes.