  We extend the generalized flux formulation of Double Field Theory to include
all the first order bosonic contributions to the $\alpha '$ expansion of the
heterotic string low energy effective theory. The generalized tangent space and
duality group are enhanced by $\alpha'$ corrections, and the gauge symmetries
are generated by the usual (gauged) generalized Lie derivative in the extended
space. The generalized frame receives derivative corrections through the spin
connection with torsion, which is incorporated as a new degree of freedom in
the extended bein. We compute the generalized fluxes and find the Riemann
curvature tensor with torsion as one of their components. All the
four-derivative terms of the action, Bianchi identities and equations of motion
are reproduced. Using this formalism, we obtain the first order $\alpha'$
corrections to the heterotic Buscher rules. The relation of our results to
alternative formulations in the literature is discussed and future research
directions are outlined.
