Morgan Stanley jumped 5.7 percent after reporting better-than-expected earnings. Goldman Sachs' profits also beat estimates, sending the stock up 3 percent. Dow-members Johnson & Johnson and UnitedHealth both posted better-than-expected earnings, sending their shares higher.

With Tuesday's sharp gains and following a rally on Friday, the Dow has risen 3 percent from the lows seen last week.

The Dow Jones Industrial Average surged 547.87 points to 25,798.42, with UnitedHealth outperforming. The gained 2.1 percent to 2,809.92 as the tech and health care sectors jumped more than 2.5 percent each. The Nasdaq Composite advanced 2.9 percent to 7,645.49. The major large-cap indexes all had their best day since March. The Russell 2000 index, which tracks small-cap stocks, jumped 2.8 percent and had its best day since Nov. 9, 2016.

Stocks rose sharply on Tuesday after the release of strong quarterly results from some of the largest U.S. companies helped the market recover from last week's sell-off.

Kim Forrest, senior portfolio manager at Fort Pitt Capital, said more companies should report stronger-than-expected earnings moving forward. "We were overly worried about the economy at the start of October," Forrest said. "I think the bar has been set pretty low by sell-side analysts."

Investors turned their eyes to Netflix after the close on Tuesday, as the company released its quarterly results. The company's earnings easily beat analyst expectations and sent Netflix shares up more than 14 percent in after-hours trading.

Investors came into the earnings season with high hopes. Analysts polled by FactSet expect third-quarter S&P 500 earnings to have grown by 19 percent.

However, Dow-component Walmart slashed its fiscal 2019 earnings forecast on Tuesday, citing its Flipkart acquisition. The earnings season comes as Wall Street tries to recover from sharp losses seen last week.

The Dow and S&P 500 fell more than 4 percent last week as worries over higher borrowing costs sent equities tumbling. The Nasdaq also fell 3.7 percent last week as tech shares dropped broadly.

But Bill Nygren, portfolio manager and chief investment officer at Harris Associates, said these worries about higher rates are misplaced.

"Over the past 50 years the 10-year bond has averaged about 6 percent and it's at about 3 percent today," Nygren told CNBC's "Halftime Report" on Tuesday. "This concern about the jiggles in the 10-year rate going up 20 or 30 basis points I think is disconnected from 50 years of history of living with a bond [yield] that was much, much higher than it is today."

Tuesday's moves come after fell in the previous session, led by tech, continuing from their overall trend last week. The S&P 500 slipped by 0.6 percent to close at 2,750.79 while the Nasdaq composite fell by 0.9 percent to end the trading day stateside at 7,430.74. The Dow also shed 89.44 points to close at 25,250.55.