The Dow Jones Industrial Average surged 754.44 points, or 2.43 percent, to 31,827.05. The S&P 500 increased 105.84 points, or 2.76 percent, to 3,936.69. The Nasdaq Composite Index added 353.10 points, or 3.11 percent, to 11,713.15.
All the 11 primary S&P 500 sectors ended in green, with communication services and industrials up 3.64 percent and 3.58 percent, respectively, leading the gains.
Investors continue to focus on the second-quarter U.S. earnings season, which broadens this week beyond the big banks.
Shares of Johnson & Johnson declined after the pharmaceutical giant reported second-quarter profit and sales that exceeded market consensus.
Shares of Hasbro advanced after the toymaker reported earnings per share that beat analyst expectations, though its revenue for the previous quarter came in lower than anticipated.
As of Tuesday morning, roughly 9 percent of S&P 500 companies have reported calendar second-quarter earnings and of those, about two-thirds have beaten analyst expectations, CNBC reported, citing statistics from data provider FactSet.
Tesla, United Airlines, and Twitter are among the major companies on deck to report later this week.
"Despite Tuesday's more positive trading session, we don't expect a sustained improvement in market sentiment until investors get greater clarity on the outlook for the economy, central bank policy, and political risks," UBS analysts said in a note.
"Uncertainty in all of these areas remains elevated," they said, adding "investors should focus on building robust portfolios that can succeed under a wide range of outcomes."
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