Trading was quiet in anticipation that the eurozone finance ministers talks could go on late and with US markets closed for the President's Day holiday.
At close, London's benchmark FTSE 100 index gained 0.68 per cent to 5,945.25 points, Frankfurt's DAX 30 rose 1.46 per cent to 6,948.25 points and in Paris the CAC 40 added 0.96 per cent at 3,472.54 points.
Elsewhere in Europe, Madrid rose 1.86 per cent, Lisbon 0.45 per cent, Amsterdam 1.42 per cent and Brussels put on 1.03 per cent.
The European single currency advanced to $1.3256 from $1.3141 in New York late on Friday, gaining ground as investors became more willing to take risks.
The dollar was at 79.48 yen, down slightly from 79.54 on Friday.
"The markets are waiting to learn more on Greece even though it looks like things are progressing well," broker Yves Marcais of Global Equities said.
"We're never safe from a bad surprise," he said, adding that trading volume was predictably low because of the US holiday closure.
Eurozone finance ministers were meeting in Brussels, seemingly agreed on tighter conditions to approve a massive rescue and avert an imminent default.
Greek Prime Minister Lucas Papademos joined talks among eurozone finance ministers to secure a 130-billion-euro ($171 billion) bailout and a writedown on privately-held debt worth 100 billion euros.
Greek Finance Minister Evangelos Venizelos said: "I am optimistic but in any case we need clear political approval from the Eurogroup."
"We have all the elements for an accord," French Finance Minister Francois Baroin said ahead of the talks that began at 1500 GMT. "That is what I will argue as finance minister this evening."
However entering the talks, Dutch Finance Minister Jan Kees De Jager demanded that the EU and IMF take "permanent" control of government decision-making over revenues and public expenditure in Greece.
Marathon negotiations have lasted for six months and have been on a knife edge in the last few weeks, with Greece appearing to totter between a rescue and eviction from the eurozone.
Most analysts consider that if Greece were to default, the consequences for the Greek people would be catastrophic, but possibly not now so dangerous for the rest of the eurozone as would have been the case last year.
"Progress out of Greece over the weekend has been the primary driver of the latest round of risk-on trade," said analyst Joel Kruger at trading website DailyFX.
"Today's Eurogroup meeting should therefore be an important moment for the process and help to at least get this saga somewhat out of the way," he said.
Asian shares mostly rose earlier on Monday, also driven by a Chinese move at the weekend to loosen monetary policy.
China's central bank said on Saturday it would cut commercial banks' reserve requirement ratio by 0.50 percentage points from February 24 to ease restrictions on lending and boost slowing economic growth.
"China continues to be a big driver behind sentiment and appetite towards risk as the world's second-biggest economy remains critical to the future of global growth and expectations," said Capital Spreads analyst Simon Denham.
"The authorities there are as desperate as everyone else to try and avoid a major meltdown or 'hard landing' of their economy, so actions like this will help in avoiding a crash."
Shanghai ended up 0.27 per cent while Hong Kong slipped back to close down 0.31 per cent on profit-taking. Tokyo shrugged off a record monthly trade deficit of 1.475 trillion yen to close up 1.08 per cent and Sydney added 1.4 per cent.