For $\gamma \in (0,2)$, $U\subset \backslash BBC$, and an instance $h$ of the Gaussian free field (GFF) on $U$, the $\gamma$-Liouville quantum gravity (LQG) surface associated with $(U,h)$ is formally described by the Riemannian metric tensor $e\gamma h(dx2+dy2)$ on $U$.
Previous work by the authors showed that one can define a canonical metric (distance function) $Dh$ on $U$ associated with a $\gamma$-LQG surface. We show that this metric is conformally covariant in the sense that it respects the coordinate change formula for $\gamma$-LQG surfaces. That is, if $U,U~$ are domains, $\varphi :U\to U~$ is a conformal transformation, $Q=2/\gamma +\gamma /2$, and $h~=h\circ \varphi -1+Q\log |(\varphi -1)\prime |$, then $Dh(z,w)=Dh~(\varphi (z),\varphi (w))$ for all $z,w\in U$. This proves that $Dh$ is intrinsic to the quantum surface structure of $(U,h)$, i.e., it does not depend on the particular choice of parameterization.