In early morning trade, London's benchmark FTSE 100 index climbed 1.08 percent to 5,877.97 points, Frankfurt's DAX 30 grew 0.61 percent to 7,203.64 points and in Paris the CAC 40 gained 0.80 percent to 3,701.13.
The London market was also cheered as global banking giant HSBC unveiled a 35-percent jump in net profits for the first half of the year.
Asian equities also powered ahead. Hong Kong rose 0.99 percent, Tokyo jumped 1.34 percent, Seoul gained 1.83 percent and Sydney advanced 1.65 percent, but Shanghai gained just 0.19 percent on poor manufacturing data.
"So we have a deal over the debt ceiling from Washington, but with President Obama calling it modest, there has to be a degree of concern that they've done little more than kick the proverbial can a bit further down the road," said IG Markets analyst Cameron Peacock.
"What's more, the package still has to be voted on and that's something that should happen in the next couple of day, but at least markets in general are finding some cheer off the news that default appears to have been averted."
US President Barack Obama announced late Sunday an 11th-hour deal to avert a potentially catastrophic US debt default that would have had a chaotic impact on the world economy.
The deal would raise the country's $14.3 trillion debt ceiling by about $2.4 trillion in two steps, while calling for roughly the same about in spending cuts over 10 years.
"I want to announce that the leaders of both parties in both chambers have reached an agreement that will reduce the deficit and avoid default, a default that would have had a devastating effect on our economy," Obama said late Sunday in Washington.
In the US Congress, leaders of the Democratic-held Senate and the Republican-led House of Representatives said they would present the framework to their rank-and-file on Monday ahead of final votes to approve the deal.
In reaction on the foreign exchange market, the dollar briefly bounced against the yen in Asian deals, but has given up most of its gains amid lingering concern over a possible US sovereign downgrade.
At 0900 GMT the euro was trading at $1.4393 compared to $1.4395 late on Friday.
"The increased probability of the US being downgraded in the near-term should weigh upon the dollar," said economist Lee Hardman at The Bank of Tokyo-Mitsubishi UFJ in London.
"Still, any relief rally in risk assets should prove short-lived with conditions still difficult given the imminent risk of a US credit downgrade which could create near-term volatility in financial markets while the global economy continues to lose momentum."
Copyright AFP (Agence France-Presse), 2011