The US Senate has passed legislation that would invalidate nondisclosure and nondisparagement agreements signed before a worker alleges sexual harassment and sexual assault.

The SPEAK Out Act (S. 4524), is backed by the policy group Lift Our Voices that was founded by former Fox News anchor Gretchen Carlson, who is bound by a nondisclosure agreement herself. The legislation has had bipartisan, bicameral support since its introduction, and was passed just before lawmakers leave town until after the midterm elections.

The Senate passed the bill, as amended, in the final moments of Thursday’s session under unanimous consent. The House...