We give a complete solution of the Eisenhart integrability conditions in three-dimensional Minkowski space obtaining 39 orthogonally separable webs and 58 inequivalent metrics in adapted coordinate systems which permit orthogonal separation of variables for the associated Hamilton-Jacobi and wave equations. The corresponding transformations from canonical separable coordinates to canonical pseudo-Cartesian coordinates are listed for each of the 58 cases and characteristic Killing tensors are given for each of the 39 webs.
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