At close on Monday London's FTSE 100 was up 1.08% and the Cac 40 in Paris by 1.14%.
The rally follows a 5% to 10% slump on most markets on Thursday and Friday on recession fears in the US and Europe.
Oil prices initially fell on hopes that Libyan crude would soon come back on tap, before rising again on greater optimism about the global economy.Business opportunities
During Asian trading hours, news from Libya combined with lingering anxiety over the economy to push the price of Brent crude futures down 3.2% to $105.15 a barrel.
By late afternoon in London, Brent was down at $1.51 a barrel to $107.11, while US sweet, light crude was up $0.74 at $83.15.Continue reading the main story Leading the rebound in stocks were the European energy firms best placed to exploit future Libyan business opportunities.
Italian oil firm ENI - the most active foreign company in Libya before the conflict began - jumped 6.33%, while France's Total rose 2.25%, and Shell climbed 2.41%.
Exploration firms Cairn Energy and Afren - both active in Africa - rose 2.95% and 4.28% respectively.
Oil industry engineering and servicing firms also received a boost from strong financial results announced by Petrofac. The UK firm rose 3.68%, while oil rigs installer Lamprell jumped 3.77%.
In Milan, other non-energy businesses did well, reflecting the close business links between Italy and Libya.
The FTSE MIB index of 40 leading stocks rose 1.7%, outstripping other European bourses.
Transport and communications firm Ansaldo - which has many contracts with Libya - jumped 5%.
US markets also joined in, with the Dow Jones starting the day more than 1% higher, before slipping back slightly.Increased supplies?
Markets are hoping that an end to the conflict in Libya will see the country's oil exports restored, increasing global supplies.
Libya is the world's 12th-largest oil exporter.
Analysts said oil prices were likely to fall further as the political situation in the country unfolds.
Before the start of the conflict, Libya produced 1.6 million barrels a day of crude oil, or about 2% of the world's output.Continue reading the main story
In the long run macroeconomic issues will play a huge role in determining which way the oil prices are headed”End Quote Avtar Sandhu Phillip Futures But as the political unrest in the country intensified, the majority of that production was hit, taking a toll on global oil supply.
"Once they get back to recovery mode, a million barrels per day are expected to enter the global supply," Jonathan Barratt of Commodity Broking told the BBC.
"This will add weight to the decline in oil prices that we have seen recently," he added.Macroeconomic factors
However, some analysts said that even though the Libyan conflict seemed to be heading towards an end, there was still uncertainty about how fast the country's oil production could be restored to the pre-conflict levels.
"It will take a long time for them to repair the production facilities and get back on track," Avtar Sandhu of Phillip Futures told the BBC.
"What we are seeing today is more of a psychological selling."
Oil prices have also been hit by concerns in the past month that demand may be hurt by a slowdown in the global economy.
On Monday, the Organisation for Economic Co-operation and Development (OECD) confirmed that growth in the world's main industrialised economies had slowed for the fourth quarter in a row during the three months to June.
The trend was most marked in the eurozone, where growth fell to 0.2% versus a year earlier, compared with 0.8% in the previous quarter.
"We can count on slower economic growth in US and Europe, and that is going to impact demand for oil," Victor Shum of Purvin and Gertz told the BBC.
Analysts said that, with two of the world's biggest economic zones struggling to boost growth, oil prices are likely to slide.
"In the long run, macroeconomic issues will play a huge role in determining which way the oil prices are headed," Phillip Futures' Mr Sandhu said.Japan threat
Markets saw heavy falls on Thursday and Friday last week on recession fears, and the negative sentiment carried over into Asian trading hours on Monday.
In Japan, the Nikkei ended the day 1% lower, although Hong Kong's Hang Seng index ended up 0.45% after a late rally.Continue reading the main story Haven investments also did well during Asian trading, but then fell back as European shares rallied.
The price of gold had risen 2.3% prior to the Europe open, to hit yet another record high, of $1,894.5 per troy ounce - before sliding sharply.
The Japanese yen held steady half-a-yen above the record level of 76.1 yen to the dollar it set on Friday.
Japan's finance minister Yoshihiko Noda reiterated the government's readiness to intervene if the currency strengthened further.
"We will watch markets even more closely than before to see whether there is any speculative activity," he said.
"We won't rule out any measures and will take decisive action when necessary."
Meanwhile, the Swiss franc - another popular haven currency - weakened against the euro. The Swiss authorities intervened last week to curtail the strength of their currency.
Currency movements are also being driven by speculation that the US Federal Reserve chairman, Ben Bernanke, will hint at further monetary stimulus measures in a major speech at Jackson Hole in Wyoming on Friday - something that is likely to weaken the dollar.