In Europe, Germany's DAX rose 1.2 percent to close at 10,029.43 while France's CAC-40 rose 1 percent to 4,489.88. Britain's FTSE 100 gained 0.7 percent to 6,865.21.
On Wall Street, the Dow traded above 17,000 for the first time, gaining 0.6 percent to 17,068.04. The S&P 500 also hit a record, rising 0.5 percent to 1,984.48.
Sentiment was further supported by the European Central Bank's reiteration that it stands ready to provide more stimulus to the economy, should it be required. For now, the bank will carry on with its recently announced measures to boost credit to businesses.
Earlier, in Asia, the Nikkei 225 index in Tokyo closed 0.1 percent lower at 15,348.29 and Hong Kong's Hang Seng inched down 0.1 percent to 25,531.44. South Korea's Kospi shed 0.2 percent to 2,010.97.
The Taiex in Taiwan gained 0.4 percent and China's Shanghai Composite edged up 0.2 percent.
In India, the Bombay Stock Exchange halted all trading early Thursday due to a network outage. It resumed trading three hours after the glitch was fixed and by mid-afternoon was up by 0.1 percent to 25,860.99.
In energy markets, the price of crude oil dropped 73 cents to $103.75 per barrel in electronic trading on the New York Mercantile Exchange. The contract fell 86 cents to $104.48 on Wednesday.
The euro dropped to $1.3609 from $1.3657 late Wednesday. The dollar rose to 102.19 yen from 101.79 yen on expectations the Fed might tighten policy sooner than expected.