"As the new week kicks off, stocks are in demand amid increased optimism over US and China reaching a trade deal and as investors anticipate stimulus measures to shore up slowing economies," noted Fiona Cincotta, analyst at City Index trading group.
"After a disastrous previous week which saw equities experience the worst week this year, risk appetite was showing strong signs of improving."
Washington and Beijing are working to revive pivotal talks aimed at ending the trade war that has roiled world markets, Trump's chief economic advisor Larry Kudlow said Sunday.
The US president himself weighed in on Twitter, saying, "We are doing very well with China, and talking!"
In another tweet, he added that the US economy was "poised for big growth after trade deals are completed," and that China is "eating Tariffs."
There remains a high level of concern about the global outlook and particularly the US economy after yields on 10-year US Treasury bonds last week slid below that of the two-year note, while the 30-year yield fell below two percent for the first time ever.
The so-called "inversion" -- when short-term interest rates are higher than longer-term ones -- is viewed as a harbinger of recession.
A majority of economists expect a US recession in the next two years, but have pushed back the onset, according to a survey Monday from the National Association for Business Economists.
The German economy could meanwhile enter a recession in the third quarter because of a "sharp" decline in industrial production held back by international trade tensions, the Bundesbank warned Monday.
"The economy could contract again slightly" this summer, Germany's central bank said in its monthly report, following a 0.1-percent decline in gross domestic product in the second quarter.
According to Germany's Der Spiegel newspaper, Angela Merkel's government is ready to boost public spending.
China has meanwhile announced an interest rate reform that it said would lower borrowing costs for companies.
"The week is off to a pleasant start, with traders seemingly buoyed by Chinese lending rate reforms and the prospect of German fiscal stimulus," said Oanda analyst Craig Erlam.
In foreign exchange, the pound dropped as the UK government expects that a no-deal Brexit on October 31 could cause food, fuel and medicine shortages.
The government's leaked readiness report found British businesses remain largely unprepared for no-deal -- despite a Bank of England survey in March finding around 80 percent judged themselves ready.
- Key figures around 1030 GMT -
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London - FTSE 100: UP 1.0 percent at 7,184.20 points
Frankfurt - DAX 30: UP 1.0 percent at 11,678.25
Paris - CAC 40: UP 0.9 percent at 5,347.41
EURO STOXX 50: UP 0.9 percent at 3,359.17
Tokyo - Nikkei 225: UP 0.7 percent at 20,563.16 (close)
Hong Kong - Hang Seng: UP 2.2 percent at 26,291.84 (close)
Shanghai - Composite: UP 2.1 percent at 2,883.10 (close)
New York - Dow: UP 1.2 percent to 25,886.01 (close)
Euro/dollar: UP at $1.1103 from $1.1089 at 2100 GMT Friday
Pound/dollar: DOWN at $1.2126 from $1.2149
Euro/pound: UP at 91.56 pence from 91.25 pence
Dollar/yen: UP at 106.54 yen from 106.36 yen
Brent North Sea crude: UP 65 cents at $59.29 per barrel
West Texas Intermediate: UP 61 cents at $55.48 per barrel