The Dow jumped 2.4 percent to close Wednesday at 12,415. The gain turned the index positive for the year and erased a 275-point plunge set off by a dismal U.S. jobs report last Friday.
Hope that Europe would help ease the region's debt crisis helped launch the rally. A news report said European officials were moving quickly to find a way to rescue Spain's hobbled banks.
In other trading, the Standard & Poor's 500 index rose 30 points to 1,315. The Nasdaq composite index jumped 67 to 2,845.
Seven stocks rose for every one that fell on the New York Stock Exchange. Trading volume was slightly higher than average at 4.1 billion shares.