In this work, a systematic investigation of the migration of sedimenting particles in a viscoelastic Couette flow is presented, using finite element 3D simulations. To this end, a novel computational approach is presented, which allows us to simulate a periodic configuration of rigid spherical particles accurately and efficiently. To study the different contributions to the particle migration, we first investigate the migration of particles sedimenting near the inner wall, without an externally-imposed Couette flow, followed by the migration of non-sedimenting particles in an externally-imposed Couette flow. Then, both flows are combined, i.e., sedimenting particles with an externally-imposed Couette flow, which was found to increase the migration velocity significantly, yielding migration velocities that are higher than the sum of the combined flows. It was also found that the trace of the conformation tensor becomes asymmetric with respect to the particle center when the particle is initially placed close to the inner cylinder. We conclude by investigating the sedimentation velocity with an imposed orthogonal shear flow. It is found that the sedimentation velocity can be both higher or lower then the Newtonian case, depending on the rheology of the suspending fluid. Specifically, a shear-thinning viscosity is shown to play an important role, which is in-line with previously-published results.