Some say the gains are premature.
"I think the market jumped the gun," Gennadiy Goldberg, an interest-rate strategist at TD Securities in New York, one of 23 primary dealers that trade with the Federal Reserve, told Bloomberg. "Today's market move is what I would have expected from a 'Remain' win tomorrow."
The British pound rallied, earlier rising above US$1.49 for the first time in 2016, even as it later pared some of those gains.
"The market is clearly now pricing in, with near certainty, a 'Remain' vote ... I do think a 'Remain' vote is more likely, but not with the degree of certainty that appears to be now priced," Adam Cole, head of G10 currency strategy at RBC Capital Markets, told Reuters.
Europe's Stoxx 600 Index finished the session with an advance of 1.3 percent from the previous close. The UK's FTSE 100 index added 1.2 percent, Germany's DAX index gained 1.9 percent, while France's CAC 40 index increased 2 percent.
Meanwhile, Tesco, Britain's largest grocer, reported an increase in UK same-store sales for the second quarter in a row, a first in more than five years, and signalled its recovery is gaining momentum.
Tesco shares closed 0.8 percent higher in London.
"We have delivered a second quarter of positive like-for-like sales growth across all parts of the group in what remains a challenging market with sustained deflation," Dave Lewis, Tesco's chief executive, said in a statement. "I am confident that the improvements we are making for customers are working and will create long-term value for our shareholders."
Some analysts were cautious.
"Tesco will be encouraged by delivering two consecutive quarters of like-for-like sales growth but the numbers are marginal, reflecting how difficult the competitive trading environment is for mainstream retailers," Jon Copestake, an analyst at the Economist Intelligence Unit, told Bloomberg.
In other retail news, shares of Macy's gained, up 1.8 percent in 3.28pm New York trading, after Terry Lundgren said he would step down as CEO next year, and Jeff Gennette, currently president, will take over.