  We extend the classical Carath\'eodory extension theorem to quasiconformal
Jordan domains $( Y, d_{Y} )$. We say that a metric space $( Y, d_{Y} )$ is a
quasiconformal Jordan domain if the completion $\overline{Y}$ of $( Y, d_{Y} )$
has finite Hausdorff $2$-measure, the boundary $\partial Y = \overline{Y}
\setminus Y$ is homeomorphic to $\mathbb{S}^{1}$, and there exists a
homeomorphism $\phi \colon \mathbb{D} \rightarrow ( Y, d_{Y} )$ that is
quasiconformal in the geometric sense.
  We show that $\phi$ has a continuous, monotone, and surjective extension
$\Phi \colon \overline{ \mathbb{D} } \rightarrow \overline{ Y }$. This result
is best possible in this generality. In addition, we find a necessary and
sufficient condition for $\Phi$ to be a quasiconformal homeomorphism. We
provide sufficient conditions for the restriction of $\Phi$ to $\mathbb{S}^{1}$
being a quasisymmetry and to $\partial Y$ being bi-Lipschitz equivalent to a
quasicircle in the plane.
