Millions more Americans will qualify for overtime pay under a final Labor Department regulation expected out Wednesday, in what could be President Barack Obama’s last big push to try to shore up workers’ wages. The rule will increase the annual salary threshold that generally determines who qualifies for overtime pay when they log more than 40 hours a week. It will have a sweeping effect on workers, employers and industries, including large and small retailers, the fast-food industry, universities and nonprofits. Analysts and industry groups expect the threshold will be doubled to about $47,000 from $23,660—a level last updated in...