We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a welldefined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz-Bismut theorem. As examples of this construction we discuss the corrections linear in α′ in heterotic strings and the absence of such corrections for type II theories.