The rally follows the Fed's commitment on Wednesday to take a "patient" approach toward raising interest rates while signaling it was on track to raise rates in 2015, which analysts said provided clarity and relief to investors over the policy outlook.

The Dow jumped 421 points and recorded the best one-day percentage gain since December 2011. The S&P 500 posted its biggest daily percentage gain since January 2013 and is up 4.5 percent for the last two sessions, making for its biggest two-day rise since November 2011.

"The anxiety over the Fed meeting has abated for now, with the Fed using that word 'patient'," said Quincy Krosby, market strategist at Prudential Financial, which is based in Newark, New Jersey. "You had the beginning of the proverbial Santa Claus rally."

A 3-percent jump in the technology sector <.SPLRCT> also helped Thursday's advance. Oracle Corp (>> Oracle Corporation) climbed 10.2 percent to $45.35, a day after quarterly results topped Wall Street expectations. Shares of Apple (>> Apple Inc.) rose 3 percent to $112.65.

Before the rally of the last two days, a selloff in oil and energy shares helped pushed the S&P 500 down nearly 5 percent from its most recent record high on Dec. 5.

"What happened this week was a game-changer. That easy money trade came to the forefront, and it's so powerful it wipes out all of these concerns that exist," said Adam Sarhan, chief executive of Sarhan Capital in New York.

The Dow Jones industrial average <.DJI> rose 421.28 points, or 2.43 percent, to 17,778.15, the S&P 500 <.SPX> gained 48.34 points, or 2.4 percent, to 2,061.23 and the Nasdaq Composite <.IXIC> added 104.08 points, or 2.24 percent, to 4,748.40.

The S&P energy sector <.SPNY> gained 2.1 percent even as U.S. crude extended its selloff since June, ending down 4.2 percent. The S&P energy sector is still down 11.2 percent for the year so far.

Investors may still be trying to recover from those losses.

"Some of those who were caught in the meat grinder of what happened with energy ... may be wanting to make up for performance now," Krosby said.

The CBOE Volatility Index <.VIX> dropped to 16.81 on Thursday from 19.44 on Wednesday, the second largest drop in December.

The upcoming quadruple-witch expiration of index futures and options on Friday also could have been behind the late-day trading rally, BGC Partners Inc equity derivatives strategist Jared Woodard said.   

If options expire when the market is on the move, traders who are short out-of-the money options have to close or hedge their exposure, he said, which tends to exaggerate gains or losses.

Volume this week has been well above the month's average. On Thursday, about 8.7 billion shares changed hands on U.S. exchanges compared with the 7.5 billion average this month, according to BATS Global Markets.

NYSE advancers outnumbered decliners 2,522 to 589, for a 4.28-to-1 ratio; on the Nasdaq, 2,093 issues rose and 655 fell, for a 3.20-to-1 ratio favoring advancers.

Among the day's gainers, Rite Aid (>> Rite Aid Corporation) shares surged 11.9 percent to $6.78 after the drugstore chain's quarterly results topped expectations and it boosted its 2015 outlook.

(Additional reporting by Saqib Ahmed; Editing by Nick Zieminski and Chris Reese)

By Caroline Valetkevitch