"Steady as she goes, with respect to policy," Kim Rupert, managing director at Action Economics in San Francisco, told Reuters. "A lot of the doves want to make sure the recovery is for real and is in place and (are) still maintaining a very accommodative posture."
In the final hour of trading in New York, the Dow Jones Industrial Average rose 0.44 per cent, the Standard & Poor's 500 Index added 0.51 per cent, while the Nasdaq Composite Index increased 0.33 per cent.
Gains in shares of Coca-Cola, up 1.3 per cent, Wal-Mart and Nike, both up 1.1 per cent, led the Dow higher.
US Treasuries also gained, pushing yields on five-year notes 5 basis points lower to 2.60 per cent.
"The Fed is getting much more realistic with regards to the slower path of growth than it had been previously - it reflects the idea that the longer-run growth path will be lower," George Goncalves, the head of interest-rate strategy at Nomura Holdings, one of the 22 primary dealers that trade directly with the Fed, told Bloomberg News.
The Fed kept its key benchmark rate steady at a record low 0.25 per cent.
"The Committee anticipates that it likely will be appropriate to maintain the current target range for the federal funds rate for a considerable time after the asset purchase program ends, especially if projected inflation continues to run below the Committee's 2 per cent longer-run goal, and longer-term inflation expectations remain well anchored," Yellen said.
Meanwhile, shares of FedEx climbed, last up 5.3 per cent, after the company lifted its full-year profit outlook. FedEx is considered an economic bellwether.
"An outstanding fourth quarter helped FedEx post solid results for fiscal 2014, and we believe we are well positioned for a strong fiscal 2015," Frederick Smith, FedEx chief executive officer, said in a statement.
In Europe, the Stoxx 600 Index ended the session with a 0.1 per cent decline from the previous close, as did France's CAC 40. Germany's DAX rose 0.1 per cent, while the UK's FTSE 100 increased 0.2 per cent.