  Superstring field theory gives expressions for heterotic and type II string
loop amplitudes that are free from ultraviolet and infrared divergences when
the number of non-compact space-time dimensions is five or more. We prove the
subleading soft graviton theorem in these theories to all orders in
perturbation theory for S-matrix elements of arbitrary number of finite energy
external states but only one external soft graviton. We also prove the leading
soft graviton theorem for arbitrary number of finite energy external states and
arbitrary number of soft gravitons. Since our analysis is based on general
properties of one particle irreducible effective action, the results are valid
in any theory of quantum gravity that gives finite result for the S-matrix
order by order in perturbation theory without violating general coordinate
invariance.
