The imbalance of normal stress around a particle induces its transverse migration in pressure-driven viscoelastic flow, offering possibilities for particle manipulation in microfluidic devices. Theoretical predictions align with experimental evidence of particles migrating towards the center-line of the flow. However, these arguments have been challenged by both experimental and numerical investigations, revealing the potential for a reversal in the direction of migration for viscoelastic shear-thinning fluids. Yet, a significant property of viscoelastic liquids that remains largely unexplored is the ratio of solvent viscosity to the sum of solvent and polymer viscosities, denoted as β. We computed the lift coefficients of a freely flowing cylinder in a bi-dimensional Poiseuille flow with Oldroyd-B constitutive equations. A transition from a negative (center-line migration) to a positive (wall migration) lift coefficient was demonstrated with increasing β values. Analogous to inertial lift, the changes in the sign of the lift coefficient were strongly correlated with abrupt (albeit small) variations in the rotation velocity of the particle. We established a scaling law for the lift coefficient that is proportional, as expected, to the Weissenberg number, but also to the difference in rotation velocity between the viscoelastic and Newtonian cases. If the particle rotates more rapidly than in the Newtonian case, it migrates towards the wall; conversely, if the particle rotates more slowly than in the Newtonian case, it migrates towards the center-line of the channel. Finally, experiments in microfluidic slits confirmed migration towards the wall for viscoelastic fluids with high viscosity ratio.