  Higher-derivative interactions and transformation rules of the fields in the
effective field theories of the massless string states are strongly constrained
by space-time symmetries and dualities. Here we use an exact formulation of ten
dimensional ${\cal N}=1$ supergravity coupled to Yang-Mills with manifest
T-duality symmetry to construct the first order $\alpha'$-corrections of the
heterotic string effective action. The theory contains a supersymmetric and
T-duality covariant generalization of the Green-Schwarz mechanism that
determines the modifications to the leading order supersymmetry transformation
rules of the fields. We compute the resulting field-dependent deformations of
the coefficients in the supersymmetry algebra and construct the invariant
action, with up to and including four-derivative terms of all the massless
bosonic and fermionic fields of the heterotic string spectrum.
