Magnetism in Co doped ZnO (ZnO:Co) is strongly affected by the presence of the ZnO's extrinsic impurities, such as unintentional hydrogen dopants. Our ab initio investigation reveals that in ZnO:Co the formation of substitutional H (H(O)) with four-fold hydrogenic bonds is favored over interstitial hydrogen (H(I)) by 0.4 eV. It is found that H(O) is trapped by Co ions to form highly stable Co-H(O)-Co complexes. H(O) also mediates a strong short-ranged ferromagnetic interaction between Co dopants via short-range exchange interaction which induces room temperature ferromagnetism.