The Republican victory raised investor hopes for more pro-business and energy-friendly policies from the US government.
The Dow Jones jumped to a new record close of 17,484.53, while the S&P 500 also finished at a record 2,023.57.
Japan’s Nikkei 225 index was up 0.4% to 17,012.71 after five days of gains.
The yen strengthened marginally against the dollar to 114.63, down from 114.69 yen in New York trade.
In Greater China, Hong Kong shares opened up 0.2% with the Hang Seng index at 23,737.76.
The benchmark Shanghai Composite index was higher 0.1% to 2,423.23 points.
In Australia, shares were trading lower 0.1% with the benchmark S&P/ASX 200 index at 5,510.20 points despite news that employment figures rebounded in October.
Government data showed that Australia added an estimated 24,100 jobs in October, recovering from a revised 23,700 drop in September. But concerns about the reliability of the data that has been revised a few times in past months weighed on investor sentiment.
Shares of struggling television channel Ten Network rose as much as over 10% in early trade after it said it had hired Citigroup to assess “strategic options” as reports surfaced of takeover offers.
In South Korea, the Kospi index was up over 0.3% at 1,937.78 points.
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