Let
$S$ be a surface,
$G$ a simply connected classical group, and
$G^{\prime }$ the associated adjoint form of the group. We show that the moduli spaces of framed local systems
${\mathcal{X}}_{G^{\prime },S}$ and
${\mathcal{A}}_{G,S}$, which were constructed by Fock and Goncharov [‘Moduli spaces of local systems and higher Teichmuller theory’, Publ. Math. Inst. Hautes Études Sci.103 (2006), 1–212], have the structure of cluster varieties, and thus together form a cluster ensemble. This simplifies some of the proofs in that paper, and also allows one to quantize higher Teichmuller space, which was previously only possible when
$G$ was of type
$A$.