  In theories of Einstein gravity coupled with a dilaton and a two-form, a soft
theorem for the two-form, known as the Kalb-Ramond B-field, has so far been
missing. In this work we fill the gap, and in turn formulate a unified soft
theorem valid for gravitons, dilatons and B-fields in any tree-level scattering
amplitude involving the three massless states. The new soft theorem is fixed by
means of on-shell gauge invariance and enters at the subleading order of the
graviton's soft theorem. In contrast to the subsubleading soft behavior of
gravitons and dilatons, we show that the soft behavior of B-fields at this
order cannot be fully fixed by gauge invariance. Nevertheless, we show that it
is possible to establish a gauge invariant decomposition of the amplitudes to
any order in the soft expansion. We check explicitly the new soft theorem in
the bosonic string and in Type II superstring theories, and furthermore
demonstrate that, at the next order in the soft expansion, totally gauge
invariant terms appear in both string theories which cannot be factorized into
a soft theorem.
