The US central bank kept interest rates on hold and said economic conditions have improved.
The Dow Jones ended 51 points higher at 18,041, while the broader S&P 500 added 3 points to close at 2,091.
But the tech-heavy Nasdaq index closed 25 points lower at 4,863, dragged lower by a fall in Apple shares.
Apple fell 6% after it reported a 13% drop in second quarter revenue on Tuesday as sales of iPhones slipped.
Twitter shares dived 16% after its latest revenues missed expectations. First quarter revenues rose 36% to $594.5m, but this was below analysts' forecasts of about $608m.
Twitter also predicted revenues of $590m to $610m for the second quarter, which was far below analysts' expectations.
Shares in Dreamworks Animation jumped 18% after reports that Comcast is in talks to buy the company. Comcast shares rose 0.4%.
After the close of trading Facebook announced that net income tripled in the first quarter to $1.5bn.
(Close): US shares clawed back early losses to close higher after investors took a positive view on the latest comments from the US Federal Reserve.