Hydrogen is a natural contaminant of SiC growth processes, and may influence the doping efficiency. Hydrogen incorporation proportional to that of boron was observed during CVD growth while the amount of hydrogen was two orders of magnitude less than the aluminum concentration. Passivation by complex formation with hydrogen has been proven both for Al and B. The experimentally observed reactivation energy of these complexes differ by 0.9 eV. Our ab initio supercell calculations in 4H-SiC indicate, that in the absence of hydrogen, boron is incorporated as isolated substitutional and prefers the carbon site, while under typical CVD conditions boron is incorporated together with hydrogen (in equal amounts), favoring the silicon site. Therefore, the presence of H is advantageous for the activation of B as a shallow acceptor. In contrast to boron, aluminum is incorporated independently of the presence of hydrogen as isolated substitutional at the silicon site. The calculated difference between the dissociation of the stable dopant plus hydrogen complexes agrees very well with experiments. Vibration frequencies for the dopant complexes have been also calculated.