The victory for pro-EU centrist Emmanuel Macron, who is now expected to beat right-wing rival Marine Le Pen in a deciding vote next month, sent the bluechip euro zone STOXX 50 index .STOXX50E up 3.9 percent, France's CAC40 .FCHI over 4 percent and bank stocks .SX7E up almost 7 percent, Reuters reported.
Traders top-sliced some of the euro's overnight gains, but it was still up more than 1 percent on the dollar EUR=EBS, more than 2 percent against the yen EURJPY= and 1.1 percent on the pound EURGBP= ahead of U.S. trading. Wall Street was also expected to jump.
"It (the first round result) has come out in line with the market's expectations so you have something of a risk rally as there was a bit of a risk-premium built into all markets," said James Binny, head of currency at State Street Global Advisors.
There was also an unwinding of safe-haven trades.
Shorter-term German bonds DE2YT=TWEB saw their biggest sell-off since the end of 2015 as investors piled back into French FR10YT=TWEB as well as Italian, Spanish, Portuguese and Greek debt.
The Japanese yen's fall was widespread JPY=EBS, the market's so-called fear-guage, the VIX volatility index .VIX, plunged the most since November and gold XAU= saw its biggest tumble of the year so far.
Macron's pledges of gradual deregulation in France and cuts in state expenditure and the civil service are the kind of talk global financial markets like to hear.
Le Pen wants to print money to finance expanded welfare payments and tax cuts, ditch the euro currency and possibly pull out of the EU, all of which raise huge uncertainties.
"Good that @EmmanuelMacron succeeded with his policy for a strong EU and social market economy. Wishing him all the best for the next two weeks," German Chancellor Angela Merkel's spokesman tweeted.
RISK MACR-ON
Futures markets pointed to a more than 1 percent rise for Wall Street which is in now in the grip of earnings season. [.N]
Investors are gearing up for the busiest result week in at least a decade, with more than 190 S&P 500 companies, including heavyweights Alphabet (GOOGL.O) and Microsoft (MSFT.O) due to report. [.N]
Asia also saw a risk rally. Japan's Nikkei .N225 jumped 1.5 percent as the yen retreated, while MSCI's broadest index of Asia-Pacific shares outside Japan .MIAPJ0000PUS edged up 0.3 percent.
Shanghai shares .SSEC fell 1.7 percent after state media signaled Beijing would tolerate more market volatility as regulators clamp down on riskier financing.
But Macron's success set the tone.
The euro jumped in relief, and was last up 1.1 percent at $1.0845 EUR=, having been as far as $1.0940, the highest since early November just after Donald Trump's U.S. election win.
The safe-haven yen slipped across the board with the euro surging as much 2.4 percent to 119.77 yen EURJPY= while the U.S. dollar gained 1.1 percent to 110.29 yen JPY=.
"I am a bit surprised by the strength of rally because this result itself is not that surprising," said Barclays' head of European research, Philippe Gudin de Vallerin.
"But we have a relief for Europe in a way that the worst case scenario has been avoided and that is why we have seen the rally in all markets," he said, adding there was also hope Macron would strengthen the key Franco-German relationship.
SCEPTICAL ON TAX
Wall Street on Friday had only a modest lift from news President Donald Trump would announce the broad outline of his proposed tax package on Wednesday.
"Markets are skeptical that the real details will be forthcoming," said analysts at ANZ in a note.
"There is also plenty of conjecture about whether any tax cuts will be able to be revenue neutral, and that could affect their ease of passage through Congress."
Investors were also keeping a wary eye on tensions in the Korean peninsula.
North Korea said on Sunday it was ready to sink a U.S. aircraft carrier to demonstrate its military might, in the latest sign of rising tension as Trump called the leaders of China and Japan to discuss the situation.
South Korea responded by asking Washington about holding joint drills with the USS Carl Vinson aircraft carrier strike group as it approaches waters off the Korean peninsula.
Oil prices recouped just a little of last week's hefty losses, still weighed by signs U.S. production and inventory growth were offsetting OPEC's attempts to reduce the global crude glut.
Brent futures LCOc1 were up 33 cents at $52.29 a barrel, while U.S. crude futures CLc1 added 30 cents to $49.92.