Let X be a compact connected Riemann surface of genus at least two. Let M-H (r, d) denote the moduli space of semistable Higgs bundles on X of rank r and degree d. We prove that the compact complex Bohr-Sommerfeld Lagrangians of M-H (r, d) are precisely the irreducible components of the nilpotent cone in M-H (r, d). This generalizes to Higgs G-bundles and also to the parabolic Higgs bundles. (C) 2015 Elsevier B.V. All rights reserved.