By Agence France-Presse
Markets were also hopeful as oil prices stabilized, Britain sealed a Brexit deal with the EU and Italy signaled a more conciliatory stance in a budget fight with Brussels.
"The main driver is that we were oversold for a short period of time," said Art Hogan, chief market strategist at B. Riley FBR after major US equity indices gained at least 1.5 percent. "We are catching up."
Stocks were hammered last week due to worries about trade wars and higher interest rates.
Hogan said investors were hoping talks between Presidents Donald Trump and Xi Jinping during this week's Group of 20 meeting in Argentina could lead to a deal.
Investors are also eyeing public remarks from top Federal Reserve officials, as well as central bank meeting minutes due to be released later this week, and hope for signs of greater caution about hiking interest rates in 2019.
- European stocks rise -
London's FTSE 100 climbed 1.2 percent after British Prime Minister Theresa May sealed a deal with 27 other EU heads on terms of Britain's divorce from the EU.
But May must now navigate the Brexit agreement through a divided parliament in which she holds the slimmest working majority -- and where lawmakers oppose it on all sides.
In Rome, Italy's populist government appeared open to reducing its draft budget deficit, fueling a surge in the Milan stock market on hopes Rome could ease a stand-off with Brussels.
"If, during the negotiating process, the deficit has to be reduced a bit, that's not a big deal," Deputy Prime Minister Luigi Di Maio told Radio Radicale.
Milan's FTSE MIB closed the day with a 2.8 percent gain. Paris and London also won at least one percent.
Bitcoin extended its slide, dropping to $3,630, down almost 15 percent from Friday.
Oil prices enjoyed a bounce for the day but had not recovered substantially from Friday's hammering, which saw WTI sink 7.7 percent and Brent lose more than six percent.
The commodity has plunged by about a third in value from four-year highs in early October due to a range of issues, including a global economic slowdown, the trade war, rising crude supplies, softer-than-expected US sanctions on Iran, stuttering business activity in China and a stronger dollar.
All eyes are now on a meeting of the Organization of the Petroleum Exporting Countries on December 6 to see if the cartel will cut output.
Key figures around 2130 GMT
New York - Dow Jones: UP 1.5 percent at 24,640.24 (close)
New York - S&P 500: UP 1.6 percent at 2,673.45 (close)
New York - Nasdaq: UP 2.1 percent at 7,081.85 (close)
Milan - FTSE MIB: UP 2.8 percent at 19,233.45 (close)
London - FTSE 100: UP 1.2 percent at 7,036.00 (close)
Frankfurt - DAX 30: UP 1.5 percent at 11,354.72 (close)
Paris - CAC 40: UP 1.0 percent at 4,994.98 (close)
EURO STOXX 50: UP 1.1 percent at 3,172.71 (close)
Tokyo - Nikkei 225: UP 0.8 percent at 21,812.00 (close)
Hong Kong - Hang Seng: UP 1.7 percent at 26,376.18 (close)
Shanghai - Composite: DOWN 0.1 percent at 2,575.81 (close)
Euro/dollar: DOWN at $1.1326 from $1.1337 at 2200 GMT Friday
Euro/pound: DOWN at 88.44 pence from 88.49 pence
Pound/dollar: DOWN at $1.2806 from $1.2814
Oil - Brent Crude: UP $1.21 at $51.63 per barrel
Oil - West Texas Intermediate: UP $1.68 at $60.48 per barrel