In Europe, Britain's FTSE 100 closed up 1 percent to 6,795.34 while Germany's DAX added 1.3 percent to 9,734.33. France's CAC-40 gained 1.5 percent to 4,369.52.
In the U.S., the Dow Jones industrial average was up 0.4 percent at 17,116 while the broader S&P 500 index rose 0.6 percent to 1,985. Upbeat earnings from Comcast and Lockheed Martin helped the mood on Wall Street.
Earlier, stock markets in Southeast Asia were mostly higher, though Indonesian shares tumbled 1.7 percent to 5,039.59 as authorities prepared to release official results of the country's hotly disputed presidential election.
Elsewhere in the region, Hong Kong's Hang Seng added 1.6 percent to 23,748.72 by mid-afternoon as investors snapped up China property shares on expectations regional governments in China will move to shore up the troubled real estate sector. China's Shanghai Composite Index rose 1 percent to 2,075.48.
Japan's Nikkei 225 stock index added 0.8 percent to 15,343.28 as trading resumed after Monday's public holiday. South Korea's Kospi gained 0.5 percent to 2,028.93.
In the currency markets, euro fell Tuesday to its lowest level against the dollar this year amid concerns that the downing of Malaysia Airlines Flight 17 will prompt a bigger freeze in relations between the European Union and Russia. The single currency fell a further 0.4 percent Tuesday to $1.3464, its lowest level since last November.