We introduce a novel approach for the investigation of spin-wave excitations in itinerant ferromagnets. Our theory is based on a variational treatment of general multi-band Hubbard models which describe elements and compounds of transition metals. The magnon dispersion is derived approximately as the energy of a variational spin-wave state in the limit of large spatial dimensions. A numerical evaluation of our results is feasible for general multi-band models. As a first application we consider a model with two degenerate orbitals per lattice site. From our results we can conclude that spin-wave excitations in strong itinerant ferromagnets are very similar to those in ferromagnetic spin systems.