We use a steady state global axisymmetric MHD model to reproduce quantitatively the Ulysses observations during its first fast latitude traversal in 1994-1995. In particular, we are able to account for the transformation of a surface dipole magnetic field near the Sun into the configuration observed at large heliocentric distances. The MHD equations are solved by combining a time relaxation numerical technique with a marching-along-radius method. We assume that Alfv¿n waves, propagating outward from the Sun, provide additional heating and acceleration to the flow. Only solutions with waves reproduce the plasma parameters observed in the high-latitude fast solar wind. We show that the meridional distribution of solar wind plasma and magnetic field parameters is dominated by two processes. First, inside ~24 R⊙ both the plasma velocity and magnetic field relax toward a latitude-independent profile outside the equatorial current sheet (where magnetic forces dominate over thermal and wave gradient forces). Second, outside ~24 R⊙ there is another meridional redistribution due to a poleward thermal pressure gradient that produces a slight poleward gradient in the radial velocity and an equatorward gradient in the radial component of the magnetic field. We reproduce the observed bimodal structure and morphology of both fast and slow wind and show that computed parameters are generally in agreement with both in situ data and conditions inferred to be characteristic of the solar corona. ¿ 2000 American Geophysical Union