The replacement of spiral bevel gears represents a challenge when the design data is missing and only the physical gears are available. In this case, application of reverse engineering is required to determine the design data and machine-tool settings that would allow the default gears to be replaced and/or improved. This paper proposes a methodology of reverse engineering of spiral bevel gears reconstructed from point clouds. Point clouds of the gear tooth surfaces are obtained from non-contact metrology machines using a 3D laser scanner . Non-uniform rational B-splines surfaces are obtained to fit a set of predefined points of the point cloud. Once the reconstructed tooth surfaces are available, a bound-constrained optimization algorithm is used to derive the finishing machine-tool settings of the gears to produce the closer tooth surfaces to the reconstructed ones. The resulting reconstructed gear drive can be analyzed throughout tooth contact and finite element analyses to evaluate its mechanical performance and improve it if necessary. A numerical example, comprising a given design of a face-milled spiral bevel gear drive and the corresponding manufactured gears, shows the advantages and disadvantages of the proposed procedure to capture the designer’s intent and analyze the existing gear drive.