News of corporate takeover activity, with Cadbury jumping over 40 percent after, also helped stocks start the week well on a day when Wall Street will be closed for the Labor Day holiday.
Germany's DAX rose 79.23 points, or 1.5 percent, to 5,463.66, while Britain's FTSE 100 gained 76.52 points, or 1.6 percent, to 4,928.22. France's CAC-40 added 50.46 points, or 1.4 percent, to 3,649.22.
Benchmarks in Japan, Hong Kong and China added about 1 percent or more after Beijing said it would allow greater access to foreign investors.
Investors reacted positively to the weekend announcements from finance officials at the Group of 20 summit in London, which acknowledged some improvements in economic growth but warned recovery was not sustainable without continued help from governments in the form of deficit spending, low interest rates and efforts to expand the money supply.
"It will come as a relief to markets that G-20 central bankers and finance ministers agreed that it was too early to begin withdrawing massive fiscal, monetary and financial support," said Mitul Kotecha, analyst at Calyon.
Markets had been worried that nascent signs of economic recovery would lead countries to unwind their stimulus, but the G-20 dispelled those fears.
"It is hardly surprising that officials are not formulating an early exit from emergency measures, especially given the ongoing uncertainty about the pace and shape of global economic recovery," said Kotecha.
He said growing doubts about the duration of an economic rebound will "pose a risk to the sustainability of any equity rally over coming months" as stocks look increasingly overvalued.
"Amongst the factors needed is some clarity about the pace and shape of growth once stimulus is reversed."
Stock markets were also helped by upbeat corporate and economic news.
Kraft Foods Inc.'s proposed £10.2 billion pounds ($16.7 billion) takeover of Cadbury PLC was immediately rejected as too low by the British maker of chocolate, gum and candy, but Kraft said it was determined to find an adequate offer. Cadbury shares shot up 40.4 percent.
"A key question is whether there is a counter bid, most likely from a Nestle-led consortium," said Graham Jones, analyst at Panmure Gordon & Co. "However, we see the most likely scenario being Kraft being successful on improved terms."
In Germany, industrial orders rose 3.5 percent on the month in July, suggesting the worst of a global slump in demand may be past for the export-dependent country.
"Despite some volatility in the data over the past few months, there is now rising evidence of a more broad-based demand for German capital goods and intermediate goods," said analysts at Calyon.
In Asia, Chinese stocks continued their recovery after the government said it would allow foreign investors to sink more money into the mainland's markets.
In Hong Kong, the Hang Seng was up 1.5 percent at 20,629.31. Shanghai's main benchmark gained 0.7 percent to 2,881.12.
Japan's Nikkei 225 stock average added 133.83 points, or 1.3 percent, to 10,320.94, snapping a three-day losing streak. Australia's index edged up 0.4 percent, Taiwan rose 1 percent and Indonesia's benchmark gained 0.4 percent. Markets in Korea and Singapore were little changed.
On Friday in the U.S., investors pushed stocks up after data showed the unemployment rate rose in August but that jobs were being cut at a slower pace.
The Dow rose 1 percent to 9,441.27, the Standard & Poor's 500 index rose 1.3 percent to 1,016.40 and the Nasdaq added 1.8 percent to 2,018.78.
Wall Street will reopen on Tuesday.
Oil prices were up in European trade, with benchmark crude for October delivery up 74 cents at $68.76, as investors looked to this week's OPEC meeting for a possible change in the cartel's production. The contract rose 6 cents Friday to settle at $68.02.
The dollar strengthened to 93.01 yen from 92.95 yen Friday night, while the euro rose to $1.4332 from $1.4309.