Tuning of the anisotropic Gilbert damping Delta alpha has been realized in ultrathin single-crystalline Fe films grown on GaAs (001). A nonmonotonic dependence of Delta alpha on film thickness t is observed upon varying t about 10 ML (similar to 1.4 nm). Delta alpha increases for 16 ML > t > 8.5 ML, and then decreases for 8.5 ML > t > 6.5 ML accompanied by a sign reversal of Delta alpha for t = 6.5 ML. The sign reversal of.a is captured by first-principle calculations, which show that the anisotropic density of states changes sign upon decreasing t. Moreover, t(-1) dependence of the anisotropic damping indicates the emergence of an anisotropic effective spin mixing conductance according to the theory of spin pumping. The results establish new opportunities for controlling the Gilbert damping and for fundamental studies of magnetization dynamics in reduced dimension.