WASHINGTON—Strong hiring and low unemployment are delivering U.S. workers their best pay raises in nearly a decade.

Employers shook off a September slowdown to add 250,000 jobs to their payrolls in October, above monthly averages in recent years, the Labor Department said Friday. With unemployment holding at 3.7%, a 49-year low, and employers competing for scarce workers, wages increased 3.1% from a year earlier, the biggest year-over-year gain for average hourly earnings since 2009.