The FTSE 100 index of leading British shares was up 0.7 percent at 6,483 while the CAC-40 in France rose 1.4 percent to 3,845. Germany's DAX was 0.9 percent higher at 8,008, its first foray above 8,000 since the start of 2008.
Wall Street was poised for solid gains, with the Dow futures and the broader S&P 500 futures up 0.6 percent.
The payrolls figures have also given the dollar a further lift as investors think the run of positive news may prompt the U.S. Federal Reserve to bring an end to its super-loose monetary policy sooner than previously thought. Looser monetary policy tends to weaken a currency.
Such expectations were also evident in the rise in the U.S. Treasury yields in the wake of the figures. The yield on the country's benchmark 10-year bond was up 0.06 percentage points at 2.06 percent.
"With the decline in the headline rate of unemployment to its lowest in five years one has to ask whether this report is one small step for employees and one giant leap for the Federal Reserve," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co.
The euro was 1.1 percent lower at $1.2963 while the dollar was 1.6 percent higher against the Japanese yen, at 96.33 yen — its first foray above 96 yen since the summer of 2009. The yen has also been on the retreat over the past few months amid expectations of a change in Japan's economic policy that will likely involve the Bank of Japan printing more money.
A lower yen has the potential to make Japanese exports cheaper and that's been at the heart of the Nikkei's recent surge. Earlier, the index jumped 2.6 percent to 12,283.62, its highest close since September 2008.
Elsewhere in Asia, Hong Kong's Hang Seng rose 1.4 percent to 23,091.95 while Australia's S&P/ASX 200 rose 0.3 percent to 5,123.40. Those in mainland China and Singapore fell.