WASHINGTON—President-elect Donald Trump is expected to tap Rep. Cathy McMorris Rodgers (R., Wash.) to lead the Interior Department, according to a person familiar with the matter.

Ms. McMorris Rodgers, a senior member of the House of Representatives, if confirmed by the Senate, would lead Mr. Trump’s efforts to open up federal lands and waters to fossil-fuel development and reverse environmental policies the Obama administration has pursued over the past eight years.

Since...