Declines in technology and tech-related heavyweight names such as Apple Inc and Netflix Inc muted gains as investors rotated out of stocks seen as safe bets following a coronavirus-led crash earlier this year.
Unofficially, the Dow Jones Industrial Average rose 454.57 points, or 1.54%, to 30,045.84, the S&P 500 gained 57.82 points, or 1.62%, to 3,635.41 and the Nasdaq Composite added 156.15 points, or 1.31%, to 12,036.79.
"Markets have been constrained by very high levels of uncertainty on the USA political front and around vaccines for weeks, so with those two going away investors are considering the prospect of a return to normality in 2021", said Emmanuel Cau, head of European equity strategy at Barclays.
After spending much of the morning amplifying weird falsehoods about the election and refusing to concede defeat even as two additional states certified his loss, President Donald Trump on Tuesday held a surprise press conference at which he bragged about the stock market for just over a minute before leaving without taking a single question from reporters.
The Mexican peso lost 0.16% versus the USA dollar at 20.18.
All three indexes rallied after the opening bell, then retreated in choppy trading, with the S&P 500 and Nasdaq both dipping briefly into negative territory, before surging again in the mid-afternoon.
Gold continued to lose its luster as well, dropping to $ 1,826.3 an ounce, having now fallen 10% this month.
Some analysts expect big, short-term risks ahead the US Thanksgiving holiday, although others say unexpected news events at the start of the shorter trading week helped investors focus on the growing positives for financial markets. Jet-engine maker Rolls Royce Holdings advanced over 7%, cruise company Carnival jumped almost 9% and International Consolidated Airlines Group, parent of British Airways, rose about 5% in London. A rise in Tesla shares took the electric carmaker's market value above $500bn (£374bn).
Brent crude futures rose 45 cents, or 1%, to $46.51 a barrel to add to a more than 20% surge this month, while US West Texas Intermediate crude added 46 cents, or 1.1%, to $43.52.
Word that Biden has chosen Yellen as treasury secretary also added to investors' confidence. It is now trading at 11848.30, down 8 points or -0.7% on the day.
United States crude recently fell 0.26 per cent to US$42.95 per barrel and Brent was at US$45.83, up 1.94 per cent on the day. Spot gold fell sharply and is now down -1.81% at $1837.
In Europe, France's CAC 40 fell 0.1%, and Germany's DAX slipped 0.1%.
The 30-year bond yield was last at 1.5954%, from 1.563% and the 2-year note was last yielding 0.1641%, from 0.169%.