Around 1330 GMT, London's benchmark FTSE 100 index was up 0.8 percent compared with Monday's close.
In the eurozone, Frankfurt's DAX 30 jumped 1.5 percent and the Paris CAC 40 won 1.2 percent.
Wall Street stocks also rose at the opening bell, with the Dow climbing 0.3 percent.
The dollar traded mixed, while bitcoin went back above $8,000 to reach the highest level since May.
"Stock markets are enjoying a decent move higher... receiving a dual boost in sentiment from a proposed Chinese fiscal stimulus and a better than expected set of results from Google-parent company Alphabet," said David Cheetham, chief market analyst at traders XTB.
Tensions persist over a potential global trade war, however, with European Commission President Jean-Claude Juncker heading to Washington on Wednesday to meet with US President Donald Trump and try to avert an escalation of tit-for-tat tariffs.
The US leader is already embroiled in a messy trade dispute with China and Europe, while negotiations with Canada and Mexico to revamp the North American Free Trade Agreement have stalled.
In a bid aimed at shielding China's economy -- the world's second-largest -- from a worsening trade row with Washington, Beijing on Tuesday signalled it would shift to a looser fiscal policy.
Chinese Premier Li Keqiang stressed the government would accelerate plans to reduce taxes by more than 1.1 trillion yuan ($160 billion) and to issue 1.35 trillion yuan in local government special bonds for infrastructure.
"The proactive move by the Chinese authorities has lifted investor confidence around the global," said David Madden, analyst at CMC Markets UK.
Shares in mining and metal companies, which stand to see more business if Chinese economic growth accelerates, dominated the leaders board on the FTSE 100, with Glencore, Rio Tinto and Anglo American all up 5 percent or more in afternoon trading.
Focus was also on the latest round of earnings reports, with the tech sector receiving a boost from Alphabet's stronger-than-expected quarterly profits announced Monday.
Amazon and Facebook will also report their results this week.
In Europe meanwhile, shares in French car giant PSA surged 12 percent after the owner of Peugeot drove profits higher thanks in part to a major turnaround for its Opel Vauxhall brand.
Elsewhere Tuesday, China's state-owned China Tower -- the world's largest operator of telecommunications towers -- announced it would aim for an $8.7-billion initial public offering in Hong Kong, the biggest globally in four years.
Oil prices pulled back after a sharp jump on Monday following sabre rattling by Iranian and US leaders.
In foreign currency trading, the Turkish lira slumped 3.5 percent against the dollar after the central bank unexpectedly kept rates on hold.
"The lira has collapsed like a house of cards against the dollar after Turkey's central bank unexpectedly held key interest rates despite rapidly rising inflation," said FXTM research analyst Lukman Otunuga.
"This move is likely to raise critical questions over the independence of the country's central bank, a month after President Erdogan's re-election," he added.