"Stocks surged amid speculation that European leaders are discussing an agreement under which eurozone member states will commit to tighter budget discipline without waiting for treaty changes," said Scott Marcouiller of Wells Fargo Advisors.
The Dow Jones Industrial Average gained 2.59 percent, or 291.23 points to reach 11,523.01 in closing trades. Amid one of the busiest days of the year for online sales, the Nasdaq was up 3.52 percent (85.83) to hit 2,527.34.
The S&P 500 was up 2.92 percent (33.88 points) to reach 1,192.55.
The broader market was also boosted by expectations that normally brisk trade on "Cyber Monday" would match last week's holiday-influenced in-store sales.
Americans shrugged off economic gloom to spend a record $52.4 billion over Thanksgiving weekend, the National Retail Federation said.
Sales over the long holiday weekend were up 16 percent from last year, marking the biggest dollar amount ever spent over the Black Friday period, the unofficial start of the Christmas shopping season, the NRF said.
"Wall Street is looking to shake off last week's drubbing," said Karee Venema of Schaeffer's Investment Research.
The Dow lost 4.8 percent last week.
Minerals, mining and manufacturing firms seemed to benefit from Monday's rally.
Alcoa and Caterpillar shares were up 4.7 percent, while Hewlett-Packard and Chevron were both up strongly.
The US bond market was flat.
The interest rate paid on 10-year US debt was at 1.96 percent, the same as Friday.
The 30-year rate was at 2.91 percent, slightly up from the 2.92 percent seen on Friday.