Wall Street's main stock indices jumped at the start of trading and held steady much of the day before finishing with a flourish. The broad-based S&P 500 ended up 3.3 percent.
"Stocks are surging, safe havens are rapidly declining, and expectations for Federal Reserve rate cuts have been dramatically scaled back," said Kathleen Brooks, research director at traders XTB.
"The market was not expecting the big change to US and China tariff rates, which is very positive for the outlook for the US and the global economy," she added.
Hong Kong's stock market closed up three percent in reaction.
Paris led the way in Europe, gaining 1.4 percent, while Frankfurt notched yet another record high, although it later gave up most of its gains.
The big gainer in the French capital was luxury giant LVMH, the maker of Louis Vuitton handbags, whose shares gained seven percent.
The dollar rallied against the euro, yen and British pound, while oil prices also moved solidly higher.
Investors have been on a rollercoaster ride since US President Donald Trump unveiled tariffs on global trading partners on April 2.
Trump had hit China with the heftiest measures -- 145 percent tariffs that prompted Beijing to impose retaliatory rates of 125 percent.
However, after two days of highly anticipated negotiations in Geneva, the two countries hailed progress towards ending a crisis that fuelled fears of a global recession.
In a joint statement, the United States said it would reduce levies to 30 percent while Chinese tariffs on American goods would be cut to 10 percent for 90 days starting on May 14.
"There isn't any hangup at the moment about this not being a permanent change," said Briefing.com analyst Patrick O'Hare.
"Market participants simply care that it represents a major de-escalation and a move to a tariff area that is at least workable for US businesses and the global trade order."
But Karsten Junius at bank J. Safra Sarasin urged caution.
"We expect financial markets to remain volatile over the coming months, as they have almost fully priced out negative economic surprises and could once again be disrupted by more serious obstacles in trade negotiations," he noted.
"In all likelihood, things may still get worse before they get better."
Investors are also awaiting the release this week of data on US inflation and retail sales, which will provide a fresh snapshot of the world's biggest economy since the tariffs were first unveiled.
- Key figures at around 2220 GMT -
New York - Dow: UP 2.8 percent at 42,410.10 (close)
New York - S&P 500: UP 3.3 percent at 5,844.19 (close)
New York - Nasdaq Composite: UP 4.4 percent at 18,708.34 (close)
Paris - CAC 40: UP 1.4 percent at 7,850.10 (close)
Frankfurt - DAX: UP 0.3 percent at 23,566.54 (close)
London - FTSE 100: UP 0.6 percent at 8,604.98 (close)
Tokyo - Nikkei 225: UP 0.4 percent at 37,644.26 (close)
Hong Kong - Hang Seng Index: UP 3.0 percent at 23,549.46 (close)
Shanghai - Composite: UP 0.8 percent at 3,369.24 (close)
Euro/dollar: DOWN at $1.1089 from $1.1250 on Friday
Pound/dollar: DOWN at $1.3173 from $1.3306
Dollar/yen: UP at 148.38 yen from 145.37 yen
Euro/pound: DOWN at 84.18 pence from 84.58 pence
Brent North Sea Crude: UP 1.6 percent at $64.96 per barrel
West Texas Intermediate: UP 3.2 percent at $61.95 per barrel
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