Transparent conducting oxides with p-type conductivity hold immense potential for various electronic applications. The role of native point defects in delafossite CuMO2 (M = Al, Ga, In) as the source of p-type conductivity has been widely acknowledged. However, understanding the primary defects governing the electrical properties and devising strategies for improvement remains a critical challenge. In this study, we employ range-separated hybrid density functional calculations to elucidate the impact of acceptor defects and their interactions with hydrogen on electrical conductivity. Our findings demonstrate that hydrogen plays a pivotal role in controlling p-type conductivity in these oxides. Our investigation reveals that the interactions between hydrogen interstitial Hi and copper vacancy VCu lead to the formation of stable complexes that are electrically inactive. Considerable binding energies are observed for Hi–VCu complexes, indicating that they are highly bound complexes with low formation energy and, thus, high concentrations under both O-rich and O-poor conditions. A second hydrogen can be bound to VCu to form 2Hi–VCu complexes, which are thermodynamically stable and function as a single donor. Furthermore, hydrogen can bind with the antisite acceptor defects, CuM, forming Hi–CuM complexes. However, the lower binding energies associated with these complexes suggest likely dissociation into isolated Hi and CuM at relatively low temperatures. By shedding light on the strong influence of hydrogen passivation of acceptor defects, this study offers valuable insights into p-type conductivity in delafossite CuMO2.