A survey of the manufacturing and services sector across the European currency union showed activity rose to a 10-month high in January. Though it showed the economy as a whole was still likely contracting, the improvement suggests a recovery may be slowly taking hold.
After a weak end to 2012, the survey has added to evidence that conditions improved at the start of this year,'' said Jennifer McKeown, senior European economist at Capital Economics.
By midafternoon in Europe, Germany's DAX stock index was up 0.4 percent at 7,665 while France's CAC 40 was 1 percent higher at 3,697. Britain's FTSE 100 was up 0.1 percent at 6,285.
Spanish and Italian indexes, which led world markets lower on Monday due to concerns over the political situation in both countries, rallied. Madrid's IBEX was 2 percent higher while the FTSE MIB in Milan was up 1.4 percent.
Wall Street rose on the open, with both the Dow and the broader S&P 500 up 0.8 percent, at 13,996 and 1,508, after upbeat economic figures.
The Institute for Supply Management said its index of activity in the services sector declined slightly to 55.2 points in January from 55.7 in December. Despite the drop, which was in line with expectations, the survey showed hiring was increasing, a positive sign for the world's largest economy.
Separate figures showed U.S. home prices jumped by the most in 6 years in December, thanks to a low supply of available homes and rising demand.
Despite the broad market rise, shares in computer maker Dell were down 2.6 percent after the company said it would pay shareholders $13.65 per share to bring the company off the stock market.
Earlier in Asia, markets mostly dropped as they responded to the losses suffered in Europe and the U.S. on Monday.
The regional heavyweight, Japan's Nikkei 225, dropped 1.9 percent to 11,046.92 while Hong Kong's Hang Seng plunged 2.3 percent to 23,148.53.
Australia's S&P/ASX 200 lost 0.5 percent to 4,882.70. The only gainer among major Asian markets was China's Shanghai Composite Index, which added 0.2 percent to 2,433.13.
China's economy is limping out of its deepest slump since the 2008 global crisis but optimism has been tempered by warnings the recovery could be threatened if trade or investment weakens.
A business group, the China Federation of Logistics & Purchasing, said its index of service industry activity rose marginally to 56.2 in January from 56.1 in December. The measure of new orders declined, which ``casts doubt on the strength of the recovery in the service sector,'' said Nomura economist Zhiwei Zhang in a report.
In other markets, the euro was flat at $1.3519, losing early gains after French President Francois Hollande said eurozone governments should help control the value of their shared currency.
The dollar rose 1 percent against the Japanese yen, to 93.27.
Elsewhere, the benchmark crude oil contract for March delivery rose 67 cents to $96.84 per barrel in electronic trading on the New York Mercantile Exchange.