The pan-European STOXX 600 benchmark climbed 0.9 percent while Britain's FTSE 100 rose by 0.7 percent.
Germany's export-oriented DAX index, which is particularly sensitive to trade issues, was up 0.5 percent, shrugging off earlier data showing that German industrial output fell unexpectedly in November for a third month running.
"Investors are encouraged by the (US-China) trade tariff discussions - mainly because these are mid-level talks and there was an unexpected attendance by Vice Premier Liu He," said Neil Campling, co-head of the global thematic group at Mirabaud Securities. "People see that as a sign that China is attaching high importance to the talks."
The United States and China will continue trade talks in Beijing for an unscheduled third day, a member of the US delegation said.
Tariffs already applied could still hurt markets. Analysts have been cutting their earnings estimates for Europe consistently since September last year.
"The risk is that when we get into earnings season the impact of a lack of conclusion so far could hit home, hard," said Campling.
Strength among retailers propped up the market.
Their sectoral index rose 2.1 percent, with gains in France's Carrefour - up 2.7 percent after a US bank upgraded its rating on the stock - more than offsetting a disappointing update from British supermarket chain Morrisons .
Bank of America Merrill Lynch analysts upgraded Carrefour to a "buy", saying 2019 could be a year of inflection for the company thanks to changes in French regulation and an improvement in the Brazilian economy. They said a sell-off in its shares because of protests in France was overdone.
Morrisons, meanwhile, fell 3.2 percent after it missed Christmas sales forecasts after weak consumer demand hit its retail and wholesale businesses.
Technology stocks also rebounded, with a fourth-quarter profit miss at Samsung failing to have much impact on a sector that was heavily hit last week by Apple's first sales warning in nearly 12 years.
The tech index was up 1.2 percent with chipmaker AMS jumping 10.8 percent.
"European tech got hit harder last week on the back of Apple than many of the Asian and US suppliers. So there is a short-term argument that the bad news is more priced into the European names," said Mirabaud's Campling.
Shares in ASML however fell 0.7 percent after Liberum analysts said the update from Samsung, the world's biggest maker of smartphones and semiconductors, provided a negative read-across for the Dutch company.
"Samsung is ASML's largest customer ... We therefore expect steady downward revisions to the revenue and earnings expectations of ASML and other equipment vendors through the course of this year," Liberum said.
Italian banks hit a three-week high after the Rome government's approval late on Monday of a decree aimed at shoring up troubled lender Carige.
Gains in the index fizzled out, though, ending the day down 0.9 percent as shares in Italy's top lenders Intesa Sanpaolo and UniCredit turned lower to close down 1.2 and 1.6 percent respectively.