After a string of weak data that fanned worries about the country's financial health and particularly its property sector, the Chinese central bank said it would cut a slew of rates to boost growth.
Enthusiasm about Beijing's move helped Wall Street to shrug off disappointing US consumer confidence data.
Following big gains in Hong Kong and Shanghai, Wall Street stocks pushed higher, lifting the Dow and S&P 500 to fresh records.
The Paris stock market led the way in Europe, closing with a 1.3 percent gain as the luxury fashion sector was boosted by hopes of rebounding Chinese demand.
China's measures "should be good news for commodity producers, stocks with links to the Chinese and Hong Kong property market, and European companies that sell to the Chinese consumer", said Kathleen Brooks, research director at broker XTB.
"This package could help the beleaguered German luxury car sector along with French luxury goods houses," she added.
Shares in German automakers surged as China is a key market for the sector, with BMW notably adding more than three percent.
Overall,Frankfurt ended the session up 0.8 percent, brushing off news that German business confidence deteriorated for a fourth straight month in September, according to a closely-watched survey.
London edged up 0.3 percent, helped by strong gains to mining groups on the news out of commodities-hungry China.
China is the world's top importer of crude and oil prices moved firmly higher.
The moves by China's central bank gave markets a renewed boost after stocks rallied last week following the US Federal Reserve's first interest rate cut in more than four years.
Shanghai and Hong Kong stock markets closed up more than four percent.
Julian Evans-Pritchard, head of China economics at Capital Economics research group, said the action by Beijing represents "the most significant stimulus package since the early days of the pandemic".
But he warned "it may not be enough", adding a full economic recovery would "require more substantial fiscal support than the modest pick-up in government spending that's currently in the pipeline".
Traders are now awaiting the release Friday of the personal consumption expenditures index -- the Fed's preferred inflation metric -- hoping for an idea about its next interest-rate move.
- Key figures around 2030 GMT -
New York - Dow: UP 0.2 percent at 42,208.22 (close)
New York - S&P 500: UP 0.3 percent at 5,732.93 (close)
New York - Nasdaq Composite UP 0.6 percent at 18,074.52 (close)
London - FTSE 100: UP 0.3 percent at 8,282.76 (close)
Paris - CAC 40: UP 1.3 percent at 7,600.17 (close)
Frankfurt - DAX: UP 0.8 percent at 18,996.63 (close)
Tokyo - Nikkei 225: UP 0.6 percent to 37,940.59 (close)
Hong Kong - Hang Seng Index: UP 4.1 percent to 19,000.56 (close)
Shanghai - Composite: UP 4.2 percent to 2,863.13 (close)
Euro/dollar: UP at $1.1181 from $1.1111 on Monday
Pound/dollar: UP at $1.3412 from $1.3347
Dollar/yen: DOWN at 143.18 yen from 143.61 yen
Euro/pound: DOWN at 83.33 pence from 83.24 pence
Brent North Sea Crude: UP 1.7 percent at $75.17 per barrel
West Texas Intermediate: UP 1.7 percent at $71.56 per barrel
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