If the current pace continues, Zandi said he expects the unemployment rate to fall near 3 percent over the next year. The headline jobless rate currently is at 3.9 percent.
The ADP/Moody's count comes two days ahead of the Labor Department's closely watched nonfarm payrolls report. Economists also expect that report to show job growth of 185,000.
The jump came despite the disruption of Hurricane Florence, which ravaged the Carolinas and was expected to dent the jobs count. The nature of ADP's methodology is such that it doesn't include the storm victims because it only counts employees on payroll and doesn't account for those displaced by temporary events.
"This overstates the case a little bit," Zandi said. He added that the actual count could come down about 25,000 once the storm impact is considered.
Job gains were spread across industries, as services led with 184,000. Professional and business services contributed 70,000, while education and health services was next with 44,000, and trade, transportation, and utilities added 30,000. Leisure and hospitality and financial services each saw growth of 16,000.
There were several weak notes, however. Manufacturing added just 7,000, its weakest reading in a year, while Zandi said retail and mortgage banking also were weak.
Businesses with between 51 and 499 employees added the most by size, with 99,000 new hires. Large businesses added 75,000 while small firms contributed 56,000.
The August private payrolls count was revised up by 5,000.
The report comes at a strong time for the economy, which is coming off 4.2 percent GDP growth in the second quarter a number that could be above 4 percent for the third quarter as well. Federal Reserve Chairman Jerome Powell in a speech Tuesday characterized the economy outlook among forecasters as "remarkably positive."
WATCH: ADP data doesn't take Hurricane Florence into account