We present and analyse a family of approximations of magneto-static problems based on the Virtual Element approach in two and three dimensions. The magnetic field H is discretized as an edge Virtual Element, and the (given) current density is interpolated as a face Virtual Element. The constitutive equation is imposed strongly, and the condition div B=0 on the magnetic induction is imposed by means of a Lagrange multiplier following the formulation of Kikuchi. We show optimal convergence rates under mild assumptions on the decomposition, and we present some numerical tests.