The index gained to 51.5 last month, from 49.6 in August, driven by a jump in new orders. A reading above 50 signals growth.
The data sent the benchmark Dow Jones industrial average higher.
The data came as other surveys showed weak manufacturing readings for Europe, the UK and China.
The ISM survey "will boost hopes that some of the recent slowdown in economic growth was just a summer phenomenon", said Paul Dales, an economist at Capital Economics.
But a separate survey by Markit suggested manufacturing activity fell to a three-year low in September.
The Markit purchasing managers' index (PMI) for manufacturing activity fell to 51.1 from 51.5 in August, indicating that growth in the sector is slowing.
The PMI measure for the third quarter was also at a three-year low.
Markit chief economist Chris Williamson said the US PMI reading indicated weakness in the sector was likely to be affecting the wider economy.
"Economic growth... looks to have slowed further from the 1.3% annualised rate seen in the second quarter, possibly even stagnating," he said.
Weak overseas demand saw new orders for exports slip at their fastest rate in 11 months.
Earlier, eurozone PMI figures had shown that the downturn in the manufacturing sector there had eased slightly in September.
US manufacturing activity gained after three months of contraction, according to the Institute for Supply Management's monthly survey.