The FTSE 100 index of leading British shares was up 35.59 points, or 0.6 percent, at 5,779.48 while Germany's DAX rose 22.58 points, or 0.4 percent, at 6.258.14. The CAC-40 in France was 27.38 points, or 0.7 percent, higher at 4,061.61.
Europe's main markets were closed Friday and Monday for the Easter break.
The main factor behind the rise was Friday's US jobs data for March. Government figures showed that the US economy added 162,000 jobs during the month, the most since the recession began.
The figures reinforced hopes about the state of the world's largest economy, and propelled the Dow Jones industrial average in the US to a fresh 52 week high during Monday's session — US stock markets were also closed Friday.
Wall Street was set to give up some of Monday's gains in the wake of last week' jobs data — Dow futures were down 12 points, or 0.1 percent, at 10,897 while the broader Standard & Poor's 500 futures fell 2.3 points, or 0.2 percent, at 1,180.80.
The big event later in the US is likely to be the release of the minutes to the last rate-setting meeting of the US Federal Reserve. Investors will be interested to see whether the Fed sounds a more optimistic tone about the US economy and whether there are signs that interest rates will start going up sooner than anticipated.
Particularly interesting will be if anyone joins Kansas City Fed President Thomas Hoenig in voting against the phrase keeping interest rates low "for an extended period."
"Barring any nasty surprises here global stock markets remain very healthy within their longer term recoveries and it does not look like it would take much to lift the Dow through 11,000 in the next couple of days," said David Jones, chief market strategist at IG Index.
Central banks will be at the forefront of attention this week, with both the European Central Bank and the Bank of England set to leave their benchmark rates at 1 percent and 0.5 percent respectively. More interest will be on what the banks say about the recovery from recession.
Earlier, the Reserve Bank of Australia surprised many in the markets by increasing its benchmark rate by a quarter percentage point to 4.25 percent and hinted that further increases are in the offing to rein in inflationary pressures.
The interest rate hike helped Australia's benchmark S&P/ASX 200 jump 0.9 percent to 4,953.70 and the Australian dollar to advance 0.3 percent higher to $0.9242.
The euro continued to suffer amid renewed concerns about Greece's debt crisis amid reports that the debt-laden country is trying to renegotiate the terms of its aid package after discovering how stringent any involvement from the International Monetary Fund would be — the single European currency was down 0.5 percent at $1.3413.
"The euro continues to be capped by concerns about sovereign debt, especially Greece as they seek to fund the next stage of their debt roll-over to the tune of about euro10 billion," said Michael Hewson, analyst at CMC Markets.
"It's also not being helped by continued disagreement amongst European leaders about the rates that Greece should be charged for any help, as Greece seeks to change the terms for any financial aid that was agreed at last months EU summit, over fears of further social unrest," Hewson added.
Meanwhile, the pound was down 1 percent at $1.5143 as Prime Minister Gordon Brown confirmed that the general election will take place on May 6.
Though his governing Labour Party is behind in all opinion polls, some are showing that the gap between the Conservatives and Labour is narrow and that a so-called hung parliament, where no one party can command a majority in the House of Commons, remains a distinct possibility.
The worry in the markets is that economic policy in a post-election coalition would not be as clear-cut than if a single party emerged triumphant. The worry is amplified if a coalition cannot be concluded and a second election looms.
Earlier in Asia, Japan's benchmark Nikkei 225 stock average fell 0.5 percent, while Indonesia's main index dropped 0.2 percent. China, South Korea and India were little changed.
Markets in Hong Kong and Thailand were closed for holidays.
Benchmark crude for May delivery was down 44 cents to $86.18 a barrel.
