WASHINGTON—The U.S. economy added more jobs than expected in July and the unemployment rate edged down, a move that should help ease concerns that a new recession may be around the corner.

Nonfarm payrolls rose by 117,000 last month as private-sector employers added 154,000 jobs, the Labor Department said Friday. Payroll data for the previous two months were revised up by a total 56,000 to show increases of 46,000 jobs in June and 53,000 in May.

The...