A new drift module has been developed in the DIVIMP code, enabling two-dimensional simulations of tungsten (W) transport in the edge plasma with full drifts included. By using the SOLPS-DIVIMP code package, the impact of drifts on W transport and screening has been investigated for various levels of dissipative divertor conditions and different divertor geometric configurations in EAST. Simulation results reveal that E ⃗×B ⃗ drifts can enhance the W leakage by more than one order of magnitude. Under the favorable Bt direction, W erosion mainly occurs on the outer divertor target, making the W leakage from the outer divertor region the dominator. A leakage path from the near-SOL region is revealed by the modeling results. In the leakage path, both the ion temperature gradient force and the reversed poloidal E ⃗×B ⃗ drift are pointing upstream. With the radial E ⃗×B ⃗ drift pushing W ions from the well-screened far-SOL region to the near-SOL region, the leakage from the near-SOL region becomes significant. As the divertor condition varies from the low-recycling regime to the deep detachment regime, the decrease of the ion temperature gradient velocity and poloidal E ⃗×B ⃗ drift velocity narrows the width of the near-SOL leakage tunnel and thus enhances W screening. While under the unfavorable Bt, W erosion and leakage from the inner divertor target matters, the leakage mechanism especially the leakage path from the near-SOL region is similar as the favorable Bt cases. Furthermore, the effect of different divertor geometries on the W screening has been investigated. The configuration with the outer strike point (OSP) on the horizontal divertor plate is proved to narrow the near-SOL leakage tunnel, and thus the unreversed poloidal E ⃗×B ⃗ drift pointing to the divertor target dominates and helps to enhance the divertor W screening. For the same D2 puffing rate, the W leakage ability of cases with the OSP on the horizontal target can be more than 10 times weaker than the cases with the OSP on the vertical target, especially when the divertor is detached.