The S&P 500 closed up 3.4% overnight, boosting Asian shares and lifting the US index nearly 11% from lows seen last week.
The S&P 500 closed at 1,195 last night, a rise of more than 39 points on the day, leaving it 10.8% above the 1,078 level reached in early trading on 4 October.
The index also closed above its 50-day moving average for the first time since July.
The Dow Jones Industrial Average rose by 330 points, or 3%, to close at 11,433 points as markets grew more confident over the likelihood of a resolution to the eurozone crisis.
In the UK, the FTSE 100 rose 1.8% to 5,399 last night, but has opened down 0.5% in early trading today.
Policymakers have set an end of the month deadline for resolving the crisis, though they have yet to provide firm details on their plans.
Markets moved higher in Asia in reaction to the more positive sentiment and the news that China was to buy equity stakes in major banks.
The Nikkei closed up 2% at 8,774 in Japan after being closed for a holiday on Monday, while the Hang Seng was up 2.2% to 18,103.
Two global vehicles
'Further plug advice gap'
Must appoint separate CEOs and boards
Advisers do come out well
Will report to Mark Till