Whole-plane SLE$_κ$ is a random fractal curve between two points on the Riemann sphere. Zhan established for $κ\leq 4$ that whole-plane SLE$_κ$ is reversible, meaning invariant in law under conformal automorphisms swapping its endpoints. Miller and Sheffield extended this to $κ\leq 8$. We prove whole-plane SLE$_κ$ is reversible for $κ> 8$, resolving the final case and answering a conjecture of Viklund and Wang. Our argument depends on a novel mating-of-trees theorem of independent interest, where Liouville quantum gravity on the disk is decorated by an independent radial space-filling SLE curve.