News of the deal, announced by Donald Trump and European Commission head Ursula von der Leyen on Sunday, followed a series of US trade agreements last week, including with Japan, and comes ahead of a new round of China-US talks.
Investors were also gearing up for a busy week of data, central bank decisions and earnings from some of the world's biggest companies.
Trump and von der Leyen announced at his golf resort in Scotland that a baseline tariff of 15 percent would be levied on EU exports to the United States.
"We've reached a deal. It's a good deal for everybody. This is probably the biggest deal ever reached in any capacity," Trump said, adding that the levies would apply across the board, including for Europe's crucial automobile sector, pharmaceuticals and semiconductors.
Brussels also agreed to purchase "$750 billion worth of energy" from the United States, as well as make $600 billion in additional investments.
"It's a good deal," von der Leyen said. "It will bring stability. It will bring predictability. That's very important for our businesses on both sides of the Atlantic."
Equities built on their recent rally, fanned by relief that countries were reaching deals with Washington.
Paris rose more than one percent at the open, with Frankfurt and London also tracking gains in Hong Kong, Shanghai, Sydney, Seoul, Wellington, Taipei and Jakarta.
Tokyo fell for a second day, having soared about five percent on Wednesday and Thursday in reaction to Japan's US deal. Singapore, Manila and Mumbai were also lower.
The broad gains came after another record day for the S&P 500 and Nasdaq on Wall Street.
"The news flow from both the extension with China and the agreement with the EU is clearly market-friendly, and should put further upside potential into the euro... and should also put renewed upside into EU equities," said Chris Weston at Pepperstone.
Traders are gearing up for a packed week, with a delegation including US Treasury Secretary Scott Bessent holding fresh trade talks with a Chinese team headed by Vice Premier He Lifeng in Stockholm.
While in April both countries imposed tariffs that reached triple-digits, US duties this year have temporarily been lowered to 30 percent and China's countermeasures slashed to 10 percent.
The 90-day truce, instituted after talks in Geneva in May, is set to expire on August 12.
Also on the agenda are earnings from tech titans Amazon, Apple, Meta and Microsoft, as well as data on US economic growth and jobs.
The Federal Reserve's latest policy meeting is expected to conclude with officials standing pat on interest rates, though investors are keen to see what their views are on the outlook for the rest of the year in light of Trump's tariffs and recent trade deals.
"We think the data supports a Fed on hold in July, but absent a significant upside surprise in the upcoming inflation data, September could be a 'live' meeting for a resumption of rate cuts, especially if economic activity data and possibly overwhelming political pressure force the Fed's hand," said Michael Krautzberger at Allianz.
The Bank of Japan is also forecast to hold off on any big moves on borrowing costs.
- Key figures at around 0715 GMT -
Tokyo - Nikkei 225: DOWN 1.1 percent at 40,998.27 (close)
Hong Kong - Hang Seng Index: UP 0.8 percent at 25,584.19
Shanghai - Composite: UP 0.1 percent at 3,597.94 (close)
London - FTSE 100: UP 0.5 percent at 9,166.60
Dollar/yen: UP at 148.00 yen from 147.68 yen on Friday
Euro/dollar: DOWN at $1.1722 from $1.1738
Pound/dollar: DOWN at $1.3417 from $1.3431
Euro/pound: DOWN at 87.37 pence from 87.40 pence
West Texas Intermediate: UP 0.9 percent at $65.76 per barrel
Brent North Sea Crude: UP 0.9 percent at $69.06 per barrel
New York - Dow: UP 0.5 percent at 44,901.92 (close)
dan/lb
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