The process of emergence of magnetic flux from the depths of the convection zone to the surface is presented in the framework of self-consistent model for the storage of field in the lower overshoot regions and as the mechanism responsible for some of the regularities observed in active regions. We have performed numerical simulations of the emergence of flux tubes in the solar convection zone including the effects of spherical geometry and rotation. The magnetic flux tubes can be stored in mechanical equilibrium in the overshoot region, which is the natural equilibrium of the flux rings in a subadiabatic layer. An undular instability leads to the formation of loops once a critical magnetic field strength of the order of 105 G is exceeded. In the nonlinear phase of their unstable evolution, the tubes move across the convection zone on a very fast time-scale, typically about one month. The geometry and dynamics of the flux tubes studied in these simulations permit prediction of some of the observed properties of the active regions. First, the wings of the tube show a marked asymmetry of inclination and velocity, which is compatible with the observed asymmetric proper motions of sunspots and with the position of the neutral line in emerging active regions. Second, upon emergence the flux tubes show a tilt angle with respect to the equator which fits reasonably well with the observed values. Third, the flux tubes rise roughly within a cone of radial directions in the Sun so that no outbreak at high latitudes takes place. The calculations lend further support to the possibility of superequipartition field strengths in the overshoot region. The implications of the present results for the dynamo mechanism are discussed and hints for observational work are also given.