The greenback recovered on Wednesday from an overnight sell-off, as Trump's victory speech eased market nerves following the surprising result of the election, Xinhua news agency reported.
Trump addressed the nation at the Hilton hotel ballroom in midtown Manhattan, saying that "I'll be a president for all Americans".
Analysts said that the increased prospect of tax cuts and a generally pro-growth set of policies from Trump, aided and abetted by the Republican clean sweep of congress, boosted investor sentiment.
The dollar index, which tracks the greenback against six major peers, was up 0.71 percent to 98.553 in late trading.
In late New York trading, the euro fell to 1.0927 dollars from 1.1020 dollars, and the British pound rose to 1.2428 dollars from 1.2393 dollars.
The dollar bought 105.69 Japanese yen, higher than 105.05 yen in the previous session. The dollar climbed to 1.3424 Canadian dollars from 1.3326 Canadian dollars.