London's benchmark FTSE 100 index climbed 0.79 percent to 5,946.60 points in early trade, with banks leading the way for a second day running.
Frankfurt's DAX 30 grew 0.47 percent to 7,324.46 points and in Paris the CAC 40 gained 0.92 percent to 3,851.79.
Share prices had already closed sharply higher on Thursday as news of the eurozone debt deal offered the hope of finally taming a crisis which has roiled markets for months.
Eurozone leaders and private creditors agreed to give Greece a new 159-billion-euro bailout, risking a potential default to prevent the debt crisis from spreading worldwide.
In foreign exchange trading, the euro dipped to $1.4406 in London deals from $1.4425 late in New York on Thursday. It had reached a two-week high of $1.4439 in the wake of Thursday's deal.
"The latest breakthrough on a second bailout for Greece is enough to keep the markets happy for the next few months," said Kathleen Brook, research director at trading group Forex.com.
"It's holiday season, people are dreaming of sandy beaches, so we think the markets will accept this plan as more of a plaster cast than a band-aid that will go some way at least to sorting out Greece's problems."
Eurozone leaders and private creditors agreed on Thursday to give Greece a new 159-billion-euro bailout, risking a potential default to prevent the debt crisis from spreading worldwide.
The eurozone and the International Monetary Fund will provide 109 billion euros while banks will share the pain with 50 billion euros up to 2014, a total equivalent to $229 billion, under the deal agreed at an emergency summit.
A deal by eurozone leaders to rescue debt-ridden Greece is a "great relief" for the country's economy and a sound guarantee for its banks, the Greek finance minister said on Friday.
"Greek banks are guaranteed and assured," Evangelos Venizelos added at a news conference in Athens.
Traders were also digesting news that business sentiment in Europe's biggest economy Germany has dropped noticeably as expectations in the manufacturing sector weakened and the climate in retailing clouded over.
The monthly Ifo business climate index dropped to 112.9 points from 114.5 points in June, ending two months of increases and falling below expectations of a decline to 113.8 points, according to a poll of economists by Dow Jones Newswires.
It was the Ifo's lowest level since October 2010, when the reading stood at 112.0 points.
Copyright AFP (Agence France-Presse), 2011