The pan-European FTSEurofirst 300 index closed up 0.1 percent, while MSCI's gauge of stocks across the globe gained 0.21 percent and hit a record closing high as well. India's Sensex gained 0.6 percent to 32,472.62.
An early flurry of activity saw the euro pop to a near two-year high versus the Japanese yen of 134.14 yen EURJPY= . "They were talking about raising interest rates for years before they did it".
JP Morgan Asset Management portfolio manager Iain Stealey said markets were now fully set for the Fed to officially announce it will cut, or taper, the amount it re-invests from the profits of its $4.2 trillion crisis-era bond portfolio.
"What may be more important to keep an eye on is the dot-plot".
Some analysts said the Fed could try to soothe some of the sting from shrinking the money supply by adjusting its economic and market forecasts to reflect a more modest trajectory of future growth and signal a more gradual pace of policy tightening.
ANALYST'S TAKE: "On the political front, no prizes for guessing that North Korea will top the agenda of President Trump's address to the gathering of world leaders at the United Nations", said Rob Carnell of ING in a report.
The lesson, investors say, is that what really matters to the bond market isn't so much what the Fed is doing, but what the policy changes mean for the USA economy in the months and years ahead.
NEW YORK, Sept 19 (Reuters) - Global stock markets edged higher on Tuesday and the dollar dipped as investors waited for signals from the U.S. "There could also be some more political action in Japan before long, as the media is suggesting that (Prime Minister Shinzo) Abe may call a snap election next month amid his rising approval rating and fragile opposition".
"There's some concern among investors as to how this will work, and how it will affect long-term rates". South Korea's Kospi added 1 percent to 2,410.83 and Sydney's S&P-ASX 200 advanced 0.5 percent to 5,724.50.
Elsewhere in Asia the mood had been more subdued.
U.S. Defense Secretary Jim Mattis hinted on Monday about the existence of military options on North Korea that might spare Seoul from a brutal counterattack.
The dollar index .DXY , which ranks the greenback versus six other major currencies, fell 0.24 percent.
After a big increase in inflation, the bank's governor Mark Carney said Thursday the chances of a hike had increased, followed on Friday by another board member signalling a move in "the coming months". Traders braced for a potential stockpile build-up expected later this week, limiting the prospect for further gains.
US crude CLcv1 fell 43 cents to settle at $49.48 a barrel, while Brent LCOcv1 declined 34 cents to settle at $55.14. Brent crude LCOc1 hovered at $55.50, not far from an nearly five-month high of $55.99 it had marked that day.