US Treasuries also gained, while the greenback fell, as the Fed maintained its forecast for a total of three rate hikes this year.
"The Fed has come to use a new term that they will use the window when they have it," Henrik Drusebjerg, chief strategist at Carnegie Investment Bank, told Bloomberg before the Fed announcement. "If the economy is strong, they will continue hiking."
The Dow advanced, led by gains in shares of UnitedHealth and those of JPMorgan Chase, up 1.3 per cent and 0.8 per cent respectively.
A report from the National Association of Home Builders/Wells Fargo showed that confidence among US homebuilders climbed in March to reach the highest level since 2005.
Oil prices rose following an Energy Information Administration report showing a surprise drop in US crude stockpiles last week, the first weekly decrease since December.
"For those looking for a rebalancing of the oil market the message is that they should be patient, and hold their nerve," the IEA said in its monthly report, according to Reuters.
In Europe, the Stoxx 600 Index finished the day with 0.4 per cent advance from the previous close. Germany's DAX Index rose 0.2 per cent, as did the UK's FTSE 100 Index and France's CAC 40 Index.
In the Netherlands, the benchmark AEX Index rose 0.3 per cent. Dutch voters headed to the polls in a general election as the latest polls showed a decline in support for Geert Wilders' anti-Islam, anti-European Union Freedom Party.