Accurate charge-carrier mobility models of amorphous organic molecular semiconductors are essential to describe the electrical properties of devices based on these materials. The disordered nature of these semiconductors leads to percolative charge transport with a large characteristic length scale, posing a challenge to the development of such models from ab initio simulations. Here, we develop an ab initio mobility model using a four-step procedure. First, the amorphous morphology together with its energy disorder and intermolecular charge-transfer integrals are obtained from ab initio simulations in a small box. Next, the ab initio information is used to set up a stochastic model for the morphology and transfer integrals. This stochastic model is then employed to generate a large simulation box with modeled morphology and transfer integrals, which can fully capture the percolative charge transport. Finally, the charge-carrier mobility in this simulation box is calculated by solving a master equation, yielding a mobility function depending on temperature, carrier concentration, and electric field. We demonstrate the procedure for hole transport in two important molecular semiconductors, α-NPD and TCTA. In contrast to a previous study, we conclude that spatial correlations in the energy disorder are unimportant for α-NPD. We apply our mobility model to two types of hole-only α-NPD devices and find that the experimental temperature-dependent current density-voltage characteristics of all devices can be well described by only slightly decreasing the simulated energy disorder strength.