WASHINGTON—Robust hiring and wage gains last month leave the Federal Reserve all but certain to raise interest rates in December and on course to continue gradually lifting them next year.

Employers added 250,000 jobs in October, the Labor Department said Friday. Workers’ average hourly earnings rose 3.1% from a year earlier—the fastest growth since 2009—while the unemployment rate held at 3.7%, matching the lowest level in 49 years.

The...