WASHINGTON—The Trump administration boosted the number of workers eligible for overtime, extending pay requirements for about 1.3 million people.

The rule, set to go into effect Jan. 1, would increase a key salary threshold below which workers generally qualify for time-and-a-half pay for logging more than 40 hours a week. That threshold would increase to $35,568 from $23,660—a figure that hasn’t changed since 2004. A more-sweeping version of the rule by the Obama administration in 2016 was blocked by a court after states...