WASHINGTON—Jelena McWilliams’s decision to resign as chairman of the Federal Deposit Insurance Corp. paves the way for Democrats to gain control of the agency’s agenda in the coming weeks, potentially leading to more-stringent requirements around bank tie-ups, climate change and other matters.

Ms. McWilliams, a Trump administration holdover, said Friday that she planned to step down, following a public fight with Democrats who now make up a majority of the FDIC board. The move comes after Ms. McWilliams had previously said she intended to serve out her full term, which lasts through mid-2023.