We have performed numerical simulations of the rise of magnetic flux tubes through the convection zone. We find that the observed proper motions of pores and sunspots in young active regions can be understood as a consequence of the Coriolis force: conservation of angular momentum leads to a retardation of the rising flux loop with respect to those parts of the flux tube that remain anchored in the overshoot layer below the convection zone proper. The result is an asymmetric shape with the following flank of the loop being more vertical than the leading part. When emerging at the solar surface, the asymmetric shape of the tube leads to proper motions which are in qualitative agreement with the observations. By studying the dependence of the asymmetry on the initial state of the flux tube we find that the observed proper motions favor a mechanical equilibrium of the magnetic field in the overshoot layer. We also find that small active regions (emerging from flux tubes with little magnetic flux) are less asymmetric and should show weaker proper motions than large bipolar regions. This prediction can be put to an observational test.