Following the original idea of Debye, we define and extract a gauge-invariant screening mass from the complex static in-medium heavy-quark potential V-Q (Q) over bar, recently obtained from lattice QCD. To this end we derive a formula using concepts from both effective-and classical field theories that faithfully reproduces both the screened real-and the imaginary part of the lattice potential with a single temperature dependent fit parameter m(D)(T). Using values of the real part of V-Q (Q) over bar in a gluonic medium, we obtain Debye masses compatible with HTL perturbation theory. (C) 2015 The Authors. Published by Elsevier B.V.