We demonstrate precise positioning of nanopores fabricated by controlled breakdown (CBD) on solid-state membranes by spatially varying the electric field strength with localized membrane thinning. We show 100 × 100 nm2 precision in standard SiN x membranes (30-100 nm thick) after selective thinning by as little as 25% with a helium ion beam. Control over nanopore position is achieved through the strong dependence of the electric field-driven CBD mechanism on membrane thickness. Confinement of pore formation to the thinned region of the membrane is confirmed by TEM imaging and by analysis of DNA translocations. These results enhance the functionality of CBD as a fabrication approach and enable the production of advanced nanopore devices for single-molecule sensing applications.