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The relative stabilities of various possible structures for hydrogen terminated GaAs͑001͒ surfaces have been studied at coverages ranging from 0.5 to 2.0 hydrogen atoms per surface gallium atom. We have used the local density approximation with a localized atomic orbital basis set and norm conserving pseudopotentials. The results are compared with experimental scanning tunneling microscopy images of these surfaces. We have also mapped the total energy of the system during recombinative desorption as a function of the hydrogen atomic coordinates and deduced thermal desorption rates from this data. It is concluded that hydrogen exposure of the GaAs(001)-c(4ϫ4) reconstructed surface leads to H-Ga terminated surfaces with a hydrogen coverage between 0.5 and 1 hydrogen atoms per surface gallium atom and mixed c(4ϫ2) and c(2ϫ2) domains. Terminal and bridging hydrogen adsorption sites are identified.