
The benchmark Nikkei 225 index, which plummeted 5.4 percent on Wednesday, shot up 6.0 percent, or 975.74 points, to 17,227.28 in the first minutes of trade.
The broader Topix index of all first-section issues was up 4.78 percent, or 62.17 points, at 1,363.33.
In forex trading, the dollar bounced back to 105.62 yen, sharply up from the 102-yen range seen when the Tokyo market closed with heavy losses on Wednesday.
Tokyo picked up a strong lead from Wall Street, where stocks surged following Trump's upset win over Hillary Clinton, with pharmaceutical and banking shares especially strong in anticipation of favourable policies.
The Dow Jones Industrial Average jumped 1.4 percent while European stocks also closed higher.
The Tokyo market saw "too much of selling yesterday although I believe that was a normal reaction" to the surprise result, said Toshihiko Matsuno, senior strategist at SMBC Friend Securities.
He added that "no-one had expected that much of rally" on Wall Street and that Trump's well-moderated attitude after his victory gave markets relief.
"Those who sold shares yesterday are buying back as they watch Trump's next steps," he said, adding hopes were currently building up on fiscal-spending plans under the Trump administration.
"We will see more swings for some time."
Rodrigo Catril, currency strategist at National Australia Bank, said: "Donald Trump's presidential win will no doubt be at the centre of investors' minds today with many pondering whether the incumbent president's bite will be as extreme as his bark."
"While a Clinton presidency was seen as providing a sense of predictability and stability, a Trump presidency is likely to bring uncertainty at least over the near term with the big question being to what extent Trump's pre-election rhetoric can or will translate into policy action next year," he said in a note.