By Agence France-Presse
The agreement raises hopes the North American Free Trade Agreement, rejected by the White House soon after Trump's election, can be salvaged after Canada rejoins talks on Tuesday.
The pact was described by the US president as "a big day for trade" and it sent the S&P 500 and Nasdaq to fresh all-time highs, while the Dow broke 26,000 for the first time since January.
Mizuho Securities said in a note to clients that investors are monitoring "the US-Canada negotiations... and the impact on US-China trade talks".
Monday's agreement comes after officials from Washington and Beijing held talks last week aimed at easing trade tensions that have seen them hit each other with tariffs on tens of billions of dollars worth of goods.
While the meeting did not achieve any breakthrough, the fact it took place was seen as a good sign.
Stephen Innes, head of Asia-Pacific trading at OANDA, said dealers were "in a festive mood" as the deal removed "one major hurdle that has been haunting North American investors for months".
He added: "Markets are revelling in any trade positives... After all, a deal is a deal."
- 'Too soon' for China talks -
However, Trump appeared to temper expectations for a fresh round of talks with China, saying after announcing the new pact that "it's just not the right time to talk right now" before adding "eventually, I'm sure that we'll be able to work out a deal".
Equities, which enjoyed a healthy run after Federal Reserve boss Jerome Powell indicated Friday the bank would not aggressively raise interest rates, mostly rose in Asia but gains from an early rally were pared.
Tokyo ended 0.1 percent higher, with Toyota boosted by news it will invest about $500 million into Uber as part of a deal to work on mass-producing self-driving vehicles.
Hong Kong was up 0.2 percent in the afternoon after jumping more than two percent Monday, while Shanghai finished 0.1 percent off.
Sydney climbed 0.6 percent and Singapore was 0.8 percent higher, with Seoul adding 0.2 percent and Taipei 0.8 percent stronger.
Manila, Wellington and Jakarta were also in positive territory.
In early European trade London rose 0.8 percent as investors returned to work after a long weekend, while Paris added 0.2 percent and Frankfurt gained 0.3 percent.
The more upbeat outlook helped high-yielding currencies. Mexico's peso jumped more than one percent on the news but struggled to maintain the gains on Tuesday, though the Canadian dollar was up 0.8 percent.
South Korea's won, the Australian dollar and the South African rand also enjoyed solid buying.
The Turkish lira weakened 0.9 percent to around 6.2 against the dollar as the country's markets reopened after a week-long holiday, with dealers continuing to fret over the financial crisis in the country.
The euro dipped but managed to hold gains that came on the back of data showing business confidence in the German economy recovered as fears over a US trade war eased.
Key figures around 0720 GMT
Tokyo - Nikkei 225: UP 0.1 percent at 22,813.47 (close)
Hong Kong - Hang Seng: UP 0.2 percent at 28,313.04
Shanghai - Composite: DOWN 0.1 percent at 2,777.98 (close)
London - FTSE 100: UP 0.8 percent at 7,635.09
Euro/dollar: DOWN at $1.1673 from $1.1680 at 2100 GMT
Pound/dollar: DOWN at $1.2870 from $1.2895
Dollar/yen: UP at 111.22 yen from 111.07 yen
Oil - West Texas Intermediate: DOWN 10 cents at $68.77 per barrel
Oil - Brent Crude: DOWN seven cents at $76.14 per barrel
New York - Dow Jones: UP one percent at 26,049.64 (close)