WASHINGTON—The Trump administration is withdrawing a decades-old air policy aimed at reining in some of the largest sources of hazardous pollutants like mercury and lead.

The Environmental Protection Agency said late Thursday it is getting rid of requirements that it forever keep sites classified as “major sources” of hazardous air pollution once they meet that classification. This “once-in always-in” policy punished industry by keeping factories and other sites under heavy regulation even if they made improvements that would...