Shares in mainland China saw solid gains on the day following the positive developments. The Shanghai composite surged 5.6 percent to 2,961.28 while the Shenzhen component added 5.587 percent to 9,134.58. The Shenzhen composite jumped 5.417 percent to 1,557.27.
Those moves took the Shanghai composite into bull market territory, or up at least 20 percent from intraday lows seen in early January. The Shanghai composite fell into a bear market, or down 20 percent from a recent high, in June 2018.
Over in Hong Kong, the Hang Seng index rose 0.52 percent in its final hour of trading. Shares of China Construction Bank gained more than 2.1 percent. Hong Kong-listed shares of Chinese network equipment firm ZTE advanced more than 2.3 percent, after leaping 13.9 percent earlier, according to Reuters.
Chinese markets in general have posted strong gains so far in 2019, the Shanghai composite, for example, is up more than 18 percent year-to-date and even the smaller CSI300 has jumped more than 20 percent year to date. That surge since the start of 2019 led investment bank UBS to caution investors that the market has gone "a long way ahead of fundamentals."
In Japan, the Nikkei 225 advanced 0.48 percent to close at 21,528.23 and the Topix rose 0.71 percent to finish its trading day at 1,620.87. Shares of index heavyweight Fast Retailing, the company behind the Uniqlo chain of apparel stores, gained 0.67 percent.
The broad MSCI Asia-ex Japan index rose 0.63 percent to 527.85 as of 3:16 p.m. HK/SIN.
"As both (the U.S. and Chinese) Presidents said significant progress has been made, the chance for the US and China to reach a deal is getting higher," OCBC Treasury Research said in a morning note. "However, the key to medium term stability hinges on two areas including agreement on China's structural reforms and the enforcement of trade deals."