The formation and relaxation dynamics of NH4(CH3OH)(m)(NH3)(n) clusters produced by photolysis of ammonia-methanol mixed clusters has been observed by a time-resolved pump-probe method with femtosecond pulse lasers. From the detailed analysis of the time evolutions of the protonated cluster ions, NH4+(CH3OH)(m)(NH3)(n), the kinetic model has been constructed, which consists of sequential three-step reaction: ultrafast hydrogen-atom transfer producing the radical pair (NH4-NH2)*, the relaxation process of radical-pair clusters, and dissociation of the solvated NH4 clusters. The initial hydrogen transfer hardly occurs between ammonia and methanol, implying the unfavorable formation of radical pair, (CH3OH2-NH2)*. The remarkable dependence of the time constants in each step on the number and composition of solvents has been explained by the following factors: hydrogen delocalization within the clusters, the internal conversion of the excited-state radical pair, and the stabilization of NH4 by solvation. The dependence of the time profiles on the probe wavelength is attributed to the different ionization efficiency of the NH4(CH3OH)(m)(NH3)(n) clusters.