In late afternoon trading in New York, the Dow Jones Industrial Average rose 0.5 per cent, the Standard & Poor's 500 Index added 0.59 per cent and the Nasdaq Composite Index advanced 0.69 per cent. Earlier in the session the Dow hit a record high 15,634.32.
Gains in shares of Bank of America and JPMorgan Chase led the Dow higher.
The US dollar weakened after the Fed statement, sliding 0.4 per cent against the euro.
"At the margin, the statement was slightly dovish," Donald Ellenberger, co-head of government and mortgage-backed securities at Federated Investors in Pittsburgh, told Bloomberg News. "In Fed jargon, they offered a slight downgrade to economic and inflation growth."
US gross domestic product, climbed at a better-than-expected 1.7 per cent annualised rate in the second quarter, following a 1.1 per cent increase the prior quarter, according to Commerce Department data released today.
Separately, private employers added a better-than-expected 200,000 jobs in July, according to the ADP National Employment Report.
"The economy is improving and the ADP report is emblematic of a pattern of growth that will continue to tilt to the upside," Eric Green, chief economist at TD Securities in New York, told Reuters. "That is enough for the Fed to taper in September."
Shares of Herbalife received a boost, last up 9.5 per cent, from a CNBC report that billionaire investor George Soros had taken a large stake in the company.
In Europe, the Stoxx 600 Index closed 0.1 per cent higher than the previous close. Germany's DAX also added 0.1 per cent, while France's CAC 40 rose 0.2 per cent and the UK's FTSE 100 increased 0.8 per cent. Both the Bank of England and the European Central Bank hold meetings on Thursday.