Oil prices rose, shrugging off a smaller-than-expected draw in US crude stockpiles, and the safe-haven yen fell against the dollar as the last pre-vote opinion polls showed the "Remain" camp holding a small lead.
Financial markets have been racked for months by worries about what Brexit, or a British exit from the European Union, would mean for Europe's stability.
"The markets are the best judge of what is going to happen, and they are saying that Britain will remain. The key is the strong jump in the pound," said Peter Cardillo, chief market economist at First Standard Financial in New York.
The pound, which has been the lightning rod for opinion on the EU referendum throughout the six-month campaign, was up 0.9per cent at $1.48 as traders cut their bets on volatility after the vote.
Wall Street rose nearly 1 per cent, with the S&P 500approaching all-time highs. MSCI's 46-country All World index climbed 1 per cent to hit its highest in two weeks.
The advance on Wall Street tracked European and Asian markets. London's FTSE rose 1.23 per cent, hitting a two-month high. Germany's DAX and France's CAC 40 rose nearly 2 per cent. In Tokyo, the Nikkei closed up 1.1 per cent.
With the polls still tight and having proved unreliable in Britain's general election last year, however, caution remained.
"Everybody is a bit shell-shocked at the way the market has moved so aggressively (towards Britain remaining in the EU),"said Saxo Bank's head of FX strategy John Hardy.
"If you are stuck with a short position, you are being forced out without even knowing the result, but what this also means is that a Brexit result is now a catastrophic risk."
- Reuters