  We report a nontrivial transition in the core structure of vortices in
two-band superconductors as a function of interband impurity scattering. We
demonstrate that, in addition to singular zeros of the order parameter, the
vortices there can acquire a circular nodal line around the singular point in
one of the superconducting components. It results in the formation of the
peculiar "moat"-like profile in one of the superconducting gaps. The moat-core
vortices occur generically in the vicinity of the impurity-induced crossover
between $s_{\pm}$ and $s_{++}$ states.
