At the close of trading in New York, the Dow Jones Industrial Average rose 0.69 percent, the Standard & Poor's 500 Index gained 0.73 percent, while the Nasdaq Composite Index added 0.44 percent.
Gains in shares of Microsoft and those of Merck, up 2.1 percent and 1.8 percent respectively, led the Dow higher.
Goldman Sachs chief Lloyd Blankfein told Bloomberg that he is optimistic about US markets. "We are in for a longish, positive market," he said.
US Treasuries fell, pushing yields on the benchmark 10-year bond three basis points higher to 2.28 percent.
"Most peoples' expectations are that we're going to get a hike by the end of the year, and the Fed [statement] today didn't do anything to change that narrative," Joe Bell, a Cincinnati-based senior equity analyst at Schaeffer's Investment Research, told Bloomberg.
While improving, the US housing sector still offers surprises of weakness too. A report showed an index of pending home sales unexpectedly declined, sliding 1.8 percent in June, following a downwardly revised 0.6 percent gain in May.
Analysts said the data is an aberration.
"The June decline is a hiccup," Jennifer Lee, a senior economist at BMO Capital Markets in Toronto, told Reuters. "It is important to bear in mind that there is still plenty of fundamental support for the housing market."
US earnings were by and large positive. Shares of General Dynamics rallied, up 4.2 percent, after the company posted profit that exceeded expectations and upgraded its full-year earnings forecast.
However, shares of Twitter plunged, down 14.5 percent, after the company reported the slowest growth in the number of its monthly average users since it went public two years ago.
In Europe, the Stoxx 600 Index ended the day with a 1 percent gain from the previous close. Germany's DAX added 0.3 percent, France's CAC 40 advanced 0.8 percent, while the UK's FTSE 100 Index rose 1.2 percent.