Directional wave speeds variations in anisotropic elastic solids enables material characterisation capabilities, such as determination of elastic constants and volumetric measurement of crystallographic texture. However, achieving such measurements is challenging especially on samples with complex geometries. Here we propose the use of Green’s Function reconstruction from diffuse ultrasonic wave fields for accurate velocity measurements on components with arbitrary geometries. Strategies for accurate reconstruction, including averaging over an increased number of different source locations, using longer window lengths of diffuse fields, and accurately deconvolving a source-dependent factor, were implemented to achieve satisfactory convergence towards Green’s Function. Additionally, low signal intensity challenges from laser interferometers were overcome to enable non-contact measurement of the wave speeds, by making use of simultaneous excitation of sources to increase signal-to-noise ratio and signal normalisation to account for energy dissipation of diffuse fields. With successful demonstration using both phased array and laser receivers, this advancement fundamentally broadens acoustic wave velocity measurement capabilities to a wider range of environments and holds promise for future material characterisation of complex-shaped components.