We show how "generalised geometry", a class of extensions of conventional differential geometry first introduced by Hitchin, gives a natural way of formulating supergravity theories. The formulation unifies the bosonic fields and symmetries and has a natural action of O(d,d) or the exceptional groups E_d in d-dimensions. By introducing the analogue of the Levi-Civita connection we find that full set of bosonic equations of motion reduce to simply the vanishing of the generalised Ricci tensor. We show that the connection also encodes the supersymmetry variations and fermionic equations of motion. This formalism also gives natural extensions of complex, symplectic and other integrable structures, with implications for describing supersymmetric string theory backgrounds.