In order to perform atomistic simulations of steel, it is necessary to have a detailed understanding of the complex interatomic interactions in transition metals and their alloys. The tight-binding approximation provides a computationally efficient, yet accurate, method to investigate such interactions. In the present work, an orthogonal tight-binding model for Fe, Mn and Cr, with the explicit inclusion of magnetism, has been parameterized from ab initio density-functional calculations.