London's FTSE 100 rose 0.7 percent, with engines-maker Rolls-Royce shooting over 10 percent higher after exceeding expectations by posting a half-year pre-tax profit of £1.94 billion ($2.57 billion), traders said.
Rolls topped the FTSE with a gain of 10.3 percent to 979 pence.
Energy giant BP, which announced a return to profit, jumped 2.4 percent.
Eurozone stock markets also rose, with Paris up 0.7 percent and Frankfurt jumping 1.1 percent percent higher as data showed growth in the bloc accelerating slightly in the second quarter to 0.6 percent.
The fresh data will reinforce hopes that despite the uncertainty and turbulence of Brexit, the eurozone is emerging from the worst of the financial crisis that began in 2008.
The growth numbers come a day after figures showed unemployment in the eurozone had dropped to its lowest level in eight years.
Despite the slew of positive data, market gains were relatively subdued as investors factored in the increased possibility of the ECB tightening monetary policy, which has sent the euro higher.
A stronger currency "is likely to make a significant dent into the revenues of those companies which generate a lot of their income from exports", said CMC Markets analyst Michael Hewson.
Despite its recent gains amid political turmoil in the White House, the euro retreated slightly against the dollar on Tuesday.
Asian stock markets meanwhile started the month on a high, boosted by strong earnings results and gathering optimism over the global economy.
Equity indexes from Shanghai to Seoul chalked up gains, with confidence fuelled by positive Chinese manufacturing data and figures showing South Korean exports surged 20 percent in July from a year earlier.
Sydney's main index recorded gains of almost one percent after Australia held interest rates at a record low of 1.50 percent.
But the central bank warned that the strengthening "Aussie" was hurting an already soft domestic economy.
Wall Street opened on the upside, with the Dow pushing further higher after having finished Monday at a fourth-straight record high, and nearing breaking through 22,000 points for the first time ever.
"US stocks are nicely higher in early action, with the global markets reacting positively to the continued mostly upbeat earnings season and favourable manufacturing data out of Europe and Asia," said analysts at Charles Schwab brokerage.
Oil prices fell with the WTI contract dropping back below $50 per barrel, having climbed above it on Monday for the first time since May amid optimism that output curbs are cutting back oversupply and reducing stockpiles.