  We construct the supersymmetric completion of E$_{6(6)}$-covariant
exceptional field theory. The theory is based on a $(5+27)$-dimensional
generalized space-time subject to a covariant section constraint. The fermions
are tensors under the local Lorentz group ${\rm SO}(1,4)\times {\rm USp}(8)$
and transform as weighted scalars under the E$_{6(6)}$ (internal) generalized
diffeomorphisms. We present the complete Lagrangian and prove its invariance
under supersymmetry. Upon explicit solution of the section constraint the
theory embeds full $D=11$ supergravity and IIB supergravity, respectively.
