Seismic Newtonian noise, arising from gravitational forces induced by density fluctuations associated with seismic wave propagation, constitutes a dominant low-frequency disturbance for underground gravitational wave detectors such as the Einstein Telescope. Since these gravitational forces cannot be shielded, accurate numerical evaluation of gravitational–seismic coupling based on computed seismic wave fields is essential for noise assessment and mitigation. This work presents a finite element formulation for the evaluation of Newtonian noise from three-dimensional seismic displacement fields defined on a finite element mesh. The gravitational acceleration acting on a test mass is obtained by numerically computing the volume and surface integrals associated with density perturbations using Gaussian quadrature. The formulation supports linear and quadratic tetrahedral and brick elements and is independent of the numerical method used to compute the seismic wave field, making it suitable for integration with existing vibration and wave-propagation models. The proposed formulation is implemented in the ANNA Newtonian Noise Analysis toolbox and is verified by means of benchmark problems for which analytical solutions are available. These include plane P- and S-waves propagating in a homogeneous elastic fullspace with a spherical cavity, as well as Rayleigh wave excitation of a homogeneous elastic half space. Excellent agreement with analytical results is obtained, and the influence of finite element discretization on accuracy is assessed. The presented framework provides a physically consistent and computationally efficient approach for noise evaluation based on seismic wave field simulations.