Investors brushed aside data showing weak first-quarter economic growth, which was tied to the severe winter that hampered exports and hit investment spending.
The Fed said in a statement it would reduce its monthly bond purchases to $45bn from $55bn, as expected.
The Dow Jones industrial average rose 45.47 points or 0.27 per cent, to 16,580.84, a record high close.
The S&P 500 gained 5.62 points or 0.3 per cent, to 1,883.95 and the Nasdaq Composite added 11.013 points or 0.27 per cent, to 4,114.556. For the month, the Dow was up 0.7 per cent, the S&P 500 was up 0.6 per cent.