We show that the zeroth cohomology of Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichm\"uller Lie algebra grt. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. Also, it allows proving the freeness part of the
Deligne-Drinfeld conjecture in some low orders. As a side result one obtains
that the homotopy deformations of the Gerstenhaber operad are parameterized by
grt. Finally, our methods give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt-elements implies the hexagon
equation.