Hennion & Walsh Asset Management Chief Investment Officer Kevin Mahn said investors took that as a "dovish" stance.
"I think what they welcomed most is that there's not going to be any sooner tapering than was originally anticipated, that there may likely only be one rate hike in 2022, and as it stands right now, only one rate hike in 2023 that only moves us up 50 basis points from where we are right now."
Stocks bounced back even before the Fed announcement as concerns eased over a default by property developer China Evergrande. Energy, tech and real estate stocks led the advance.
The Dow, S&P 500 and Nasdaq added roughly 1%.
Shares of FedEx were the biggest decliner on the S&P, descending 9%. The package courier slashed its full year earnings forecast. The company is struggling with a labor shortage that drives up costs and slows deliveries.
Chevron was the second leading gainer on the Dow, rising nearly 3%. Oil prices climbed, driving up energy stocks, after industry data showed U.S. crude stocks fell more than expected last week in the wake of two hurricanes.