The Sterile Insect Technique (SIT) is a biological control method used to reduce or eliminate pest populations or disease vectors. This technique involves releasing sterilized insects that, upon mating with the wild population, produce no offspring, leading to a decline or eventual eradication of the target species. We incorporate a spatial dimension by modeling the pest/vector population as being distributed across multiple patches, with both wild and released sterile insects migrating between these patches at predetermined rates. This study has two primary objectives: first, within an n-patch model, sufficient conditions are derived for achieving the elimination of the wild population through SIT, whether releases occur in a subset of patches or across all patches. Second, we focus on the two-patch scenario, showing that optimal SIT control within one patch can successfully reduce the wild population in that patch to a desired level within a finite time frame, provided that the migration rates between patches are sufficiently low. Numerical simulations are employed to illustrate these results and further analyze the outcomes.