The Dow Jones industrial average jumped 232 points to 13,336 shortly after the opening bell Tuesday, the first trading day of 2013. That's a gain of 1.8 percent.
The Standard & Poor's 500 index shot up 29 points, or 2 percent, to 1,455 at the open. The Nasdaq composite rose 82 points, or 2.7 percent, to 3,102.
Investors have been keeping a close eye on the budget stalemate in Washington and were relieved that a deal was reached.
However the late-night budget agreement leaves many issues unresolved and it remained unclear how long the market rally would last.
Next up is a fight over the government's borrowing limit.
<< AT LEFT, The latest market numbers, updated each minute by the Wall Street Journal