After just under half an hour of trading, the Dow Jones Industrial Average was up 2.6 percent, the broad-based S&P 500 was up 1.7 percent and the tech-heavy Nasdaq Composite was up 2.1 percent.
In the elections for the House of Representatives and Senate, Democrats made major gains at the expense of President Donald Trump's Republicans.
Several health insurers and healthcare companies are having a good day, as they could benefit from more Democratic policies.
Several major technology companies, including Alphabet, Amazon and Microsoft, are also up on Wednesday, by between 3.7 and 7.6 percent.
Trump Media & Technology Group (TMTG), which owns the social network Truth Social and is controlled by the president's family, is down 10.4 percent.
Electric carmaker Tesla and space company SpaceX, led by Donald Trump ally Elon Musk, are down 4 and 3.2 percent, respectively.
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