Following the S&P 500's rise to yet another record high on Wednesday, Asian equities posted strong gains - Japan's Nikkei 225 .N225 hit its highest since late January - and European bourses also opened sharply higher.
Investors' sanguine interpretation of the Fed's outlook was reflected in another collapse in market volatility. The VIX measure of implied volatility on Wall Street, the so-called "fear index", and major foreign exchange volatility measures hit 7-year lows.
The big loser in the wake of the Fed's policy statement and Chair Janet Yellen's press conference was the dollar. It fell against major and emerging market currencies, in tandem with U.S. Treasury yields, hitting a five-year low against sterling.
"The Fed managed to navigate through what some had expected to be a potentially tricky announcement by providing further fuel for both equity and Treasury market bulls - quite an achievement given both are already at levels that leave skeptics perplexed," Rabobank analysts said in a note to clients on Thursday.
In early trading Thursday, the FTSEurofirst 300 .FTEU3 index of leading European shares was up two thirds of a percent at 1,396 points.
Germany's DAX .GDAXI was up three quarters of a percent at 10,003 points, within 30 points of its record high. Britain's FTSE 100 .FTSE was up 0.7 percent at 6,825 points and France's CAC 40 .FCHI was also up 0.7 percent at 4,561 points.
The top blue-chip gainer in Europe was Rolls Royce RR.L, with the engine maker up more than 6 percent after it announced a one billion pound ($1.69 billion) share buyback.
Earlier in Asia, Japan's Nikkei 225 surged 1.6 percent to 15,361 points, and MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS gained 0.8 percent.
The Fed on Wednesday slashed its 2014 growth forecast but expressed confidence that the economy will continue to recover steadily in the coming years, which could warrant a slightly more aggressive pace of interest rate hikes when they start.
But that probably won't be until the middle of next year, and Yellen dismissed the recent rise in inflation to its highest in over a year as "noise".
"There were those speculating that the Fed would have to come up with a more hawkish commentary and obviously they have been disappointed," said Neil Mellor, a currency strategist with Bank of New York Mellon in London.
"Nothing has really changed from the past few days, so there will be a propensity to buy some euros, and probably sterling in lockstep with that," he said.
The dollar index .DXY, a gauge of the greenback's strength against a basket of key currencies, fell 0.4 percent to 80.25.
The dollar fell 0.1 percent against the yen to 101.75 yen JPY=, the euro rose 0.2 percent to $1.3620 EUR= and sterling hit a five-year high of $1.7018 GBP=.
Turkey's lira TRY= and South Africa's rand ZAR= were among the emerging market currencies to take heart from the Fed's policy stance.
In bonds, the benchmark 10-year Treasury note yield US10YT=RR fell to as low as 2.575 percent, its lowest in a week.
In commodities, Brent crude LCOc1 rose to a nine-month high of $114.80 a barrel hit on persistent worries over oil exports from war-torn Iraq, where Islamic militants seized much of its northern region as Baghdad's forces crumbled. O/R
Brent was poised for a third day of gains following a rise of more than 4 percent last week, with Iraqi government forces battling Sunni militants for control of the country's biggest refinery.
(Reporting by Jamie McGeever, additional reporting by Patrick Graham; Editing by Toby Chopra)
By Jamie Langer