Wall Street ended the day solidly higher Tuesday, following European bourses higher after a moderately successful Spanish bond auction and on speculation about more Federal Reserve stimulus.

The Dow Jones Industrial Average ended the day at 12,837.33, up 95.51 points (0.75 percent).

The rally started early in the day amid a "downtick in Spain's debt yields, solid gains by Europe's major bourses, and a recent run-up by the euro," according to Briefing.comanalysts.

At a Tuesday auction, Spain's Treasury succeeded in raising 3.04 billion euros ($3.8 billion), beating its target 2.0-3.0-billion-euro target in an auction of 12- and 18-month notes.

Although it still had to pay sky-high rates to lure investors -- 5.074 percent for 12-month debt and 5.107 percent for 18-month debt -- that was seen as a moderate success.

After the auction Spain's IBEX 35 index was up 2.7 percent, Britain's FTSE 100 Index was up 1.7 percent, France's CAC 40 was up 1.7 percent and Germany's the DAX was up 1.8 percent.

In the United States the rally was also spurred on by the prospect of more monetary stimulus.

The Federal Reserve on Tuesday began another crunch policy meeting, with many on Wall Street betting it steps in with more cash to stop the US economy from stalling.

By the end of trade the S&P 500 hit 1,357.98, up 13.20 points (0.98 percent).

The Nasdaq reached 2,929.76, up 34.43 points or 1.19 percent.

The prospect of better, or less bad, news from Europe spelt good news for financial stocks.

Bank of America was up 4.5 percent and JPMorgan Chase was up 2.2 percent.

Meanwhile Microsoft shares were up 2.9 percent after the company release its "Surface" tablet to compete against Apple's iPad.

The market for US bonds weakened amid improved confidence in more risky higher-yielding investments.

The yield on 10-year treasuries was up 0.04 points to 1.62 percent. On the 30-year it rose 0.05 points to 2.73 percent.

Bond yields go up as the price goes down.