Analysts had predicted that stocks would rebound at some point after the S&P 500 shed more than five per cent over two days following the shock Brexit vote. Some had viewed the market as oversold in the short run.
Especially strong sectors included banks, technology, energy and airlines.
All had experienced bigger-than-average drops during the selloff.
The Dow Jones Industrial Average rose 1.6 per cent to 17,409.72.
The broad-based S&P 500 gained 1.8 per cent at 2,036.09, while the tech-rich Nasdaq Composite Index jumped 2.1 per cent to 4,691.87.
Analysts cautioned that Tuesday's rally might not have staying power and US markets could see more volatility if European markets go through another bout of selling.
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"We retraced about one third of the move downward and we still have as many questions as we did two days ago," said Art Hogan, chief market strategist at Wunderlich Securities.
Analysts do not expect the US economy to be as directly impacted by Brexit as Europe, although a stronger dollar would challenge American companies that rely on exports.
Banking shares were upward bound, with Bank of America and JPMorgan Chase gaining 4.3 per cent and 3.3 per cent, respectively.
Energy stocks benefited from a jump in oil prices. ExxonMobil advanced 2.3 per cent and Schlumberger 2.1 per cent.
Delta Air Lines climbed 3.9 per cent and United Continental rose 3.2 per cent.
Technology stocks that gained included Apple, up 1.7 per cent, Facebook 3.4 per cent and Microsoft 2.1 per cent.
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Oil prices rebound
Oil prices rose Tuesday, benefitting from the same bounce that lifted equity markets which had been sagging since Britain's surprise decision to leave the European Union.
Thursday's Brexit vote not only sent worldwide financial markets skidding, oil prices also retreated and the British pound plunged to a 30-year low.
But analysts have been expecting a reversal of those trends at some point.
"After the bloodletting across energy commodities, equities and various currencies in recent days, today is the day we have a relief rally, with markets seeing an inevitable rebound," said analyst Matt Smith of ClipperData.
"There were outsized reactions in all capital markets following the surprising Brexit vote," said Briefing.com analyst Patrick O'Hare.
"There is a budding belief at this juncture, then, that things got overdone on a short-term basis, so there is some bargain-hunting activity taking place in oversold markets and some profit-taking occurring in overbought markets."
US benchmark West Texas Intermediate for August delivery gained $1.52 to $47.85 a barrel on the New York Mercantile Exchange.
Brent North Sea oil for delivery in August gained $1.42 to $48.58 a barrel in London.
Tuesday's movements also ended the dollar's streak of gains in the wake ofBrexit.
A weaker dollar boosts demand for oil, which is sold in the US currency on international markets.
Analysts said the oil market was boosted by worries about a potential strike in Norway's oil industry, which could affect just under 20 per cent of the Scandinavian country's oil production.
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