WASHINGTON—U.S. workers received their biggest pay increases in nearly a decade over the 12 months through June, a sign the strong labor market is boosting wages as employers compete for scarcer workers.

The Labor Department’s employment-cost index rose 2.8% in the year to June compared, the government said Tuesday. Wages and salaries, which account for about 70% of all employment costs, also rose 2.8% from a year earlier, the strongest gain for both measures since September 2008.

Since...