High-field magnetic white dwarfs have been long suspected to be the result of stellar mergers. However, the nature of the coalescing stars and the precise mechanism that produces the magnetic field are still unknown. Here, we show that the hot, convective, differentially rotating corona present in the outer layers of the remnant of the merger of two degenerate cores can produce magnetic fields of the required strength that do not decay for long timescales. Using a state-of-the-art Monte Carlo simulator, we also show that the expected number of high-field magnetic white dwarfs produced in this way is consistent with that found in the solar neighborhood.