  We prove that the SLE$_\kappa$ loop measure arises naturally from the
conformal welding of two $\gamma$-Liouville quantum gravity (LQG) disks for
$\gamma^2 = \kappa \in (0,4)$. The proof relies on our companion work on
conformal welding of LQG disks and uses as an essential tool the concept of
uniform embedding of LQG surfaces. Combining our result with work of Gwynne and
Miller, we get that random quadrangulations decorated by a self-avoiding
polygon converge in the scaling limit to the LQG sphere decorated by the
SLE$_{8/3}$ loop. Our result is also a key input to recent work of the first
and third coauthors on the integrability of the conformal loop ensemble.
