We develop the off-shell nilpotent finite field dependent Becchi-Rouet-Stora-Tyutin (BRST) transformations and show that for different choices of the finite field dependent parameter these transformations connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST transformations for Yang-Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the nontrivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results. C