WASHINGTON—President-elect Donald Trump’s transition team promised to dismantle the 2010 Dodd-Frank law, declaring that the coming administration will seek to remake the way the U.S. oversees the financial sector.

Tuesday’s Republican sweep, and Mr. Trump’s commitment to focus on the issue, has the GOP salivating over a wish list of Dodd-Frank changes that until recently stood little chance of avoiding President Barack Obama’s veto pen. The lineup includes everything from regulatory exemptions for community banks and regional...