The intensity of atmospheric storms is strongly influenced by ocean temperature contrasts. While mesoscale sea surface temperature anomalies (with a size > 50 km) are known to intensify storms via an enhancement of latent heat release, the role of finer oceanic scales remains unknown. Using a groundbreaking global coupled ocean-atmosphere simulation at a km-scale resolution, we show that both ocean mesoscales and submesoscales (with a size < 50 km) account for half of the moisture flux variability at the air-sea interface. In addition, ocean submesoscale fronts drive a secondary circulation, which extends above the planetary boundary layer up to 4 km within the troposphere, and enhance diabatic processes and convective precipitations within storms. In the warm sector of storms, ocean submesoscale fronts account for half of the total diabatic heating and half of the total precipitations, averaging 14 mm/day over five days. In contrast, diabatic heating and precipitations associated with submesoscale fronts are respectively three and twelve times smaller in the cold sector. As such, ocean submesoscale fronts pump humidity from the ocean to the atmosphere and have the potential to further warm the atmosphere, intensify storms, and influence weather patterns such as atmospheric rivers.