At lunchtime, local time, Tokyo's important Nikkei 225 index had increased by 8.1 percent, while the broader Topix index was up 7.3 percent.
The South Korean Kospi index also started the day in a fairly good mood and rose 5.3 percent at lunch. Nor was there a lack of optimism in Taiwan, where the Taiex index surged more than 9.2 percent.
It was also cheerful in Australia, where the ASX 200 index rose 4.6 percent.
Trump's announcement meant a pause on tariffs – in addition to the basic tariffs – for all countries except China. Despite this, the Chinese stock exchanges also opened on a positive note.
The Hong Kong Hang Seng index was up 1.9 percent, while Shanghai's and Shenzhen's composite index rose 0.9 and 2.5 percent, respectively.
