The Dow Jones industrial average added about 65 points, with Disney contributing the most gains, putting it within 100 points of 20,000. The Nasdaq composite advanced about 0.9 percent.
The S&P 500 gained around 0.5 percent and briefly break above its previous closing high, with consumer discretionary and materials rising more than 1 percent. "That shows that people are bottom-fishing," said Kim Forrest, senior equity analyst at Fort Pitt Capital. "Those retail stocks have gotten way oversold recently."
The minutes showed the central bank is concerned about a strengthening, and that more fiscal stimulus could raise demand above sustainable levels. Investors were looking for clues about what the central bank thought of President-elect Donald Trump's proposed fiscal policy measures. The Fed raised rates at its last meeting for just the second time in a decade and forecast three rate hikes for 2017.
"To some extent, [the minutes] reinforce the positive notion that we'll see more growth," said Bruce McCain, chief investment strategist at Key Private Bank. "That's the glass-half-full view the market seems to be taking."
That said, Mike Bailey, director of research at FBB Capital Partners, said "I do think there are some stocks with rising execution risk," meaning that certain stocks could fall if Trump does not deliver.
Mortgage applications tanked 12 percent for last week, from two weeks earlier as rising interest rates weighed.
Meanwhile, Fiat Chrysler, Ford Motor and General Motors all reported better-than-expected auto sales for December, sending their stocks higher. The annualized selling rate is expected to be around a strong 17.5 million.
"You add that with yesterday's ISM manufacturing number, which was the best in a few years, and you've got a case for strong economic growth, not just domestically but globally," said Bruce Bittles, chief investment strategist at Baird.
Investors also kept an eye on the U.S. dollar, which pulled back from its highest levels in 14 years. The greenback traded 0.4 percent lower against a basket of currencies, with the euro near $1.046 and the yen around 117.6.
Lukman Otunuga, research analyst at FXTM, said in a note that "dollar strength may become the new norm this quarter as the combination of repeatedly positive economic data and prospects of higher US rates attract investors to the currency."
"With the Trump effect still fuelling the bull rally and optimism rising over fiscal stimulus boosting US economic growth, the Dollar may be destined to be a champion amongst other major currencies once again," he said.
Japanese equities soared on the back of the dollar's weakness and strong domestic economic data. The Nikkei 225 skyrocketed 2.51 percent, while the Topix spiked 2.37 percent.
U.S. Treasurys traded mixed, with the benchmark 10-year yield at 2.454 percent, while the short-term two-year note yield advanced to 1.234 percent.
The S&P 500 gained 12 points, or 0.57 percent, to 2,270, with materials leading nine sectors higher and telecommunications and energy declining.
The Nasdaq composite advanced 50 points, or 0.9 percent, to trade at 5,479.
About five stocks advanced for every decliner at the New York Stock Exchange, with an exchange volume of 487 million and a composite volume of 2.514 Billion in afternoon trade.
The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, traded near 11.9.
Earnings: Monsanto, Walgreen Boots Alliance, Constellation Brands, Ruby Tuesday, PriceSmart
8:15 a.m. ADP employment
8:30 a.m. Initial claims
9:45 a.m. Services PMI
10 a.m. ISM nonmanufacturing
8:30 a.m. Employment
8:30 a.m. International trade
10 a.m. Factory orders
11:15 a.m. Chicago Fed President Charles Evans
1:00 p.m. Richmond Fed President Jeffrey Lacker
3:30 p.m. Dallas Fed President Robert Kaplan
11:15 a.m. Federal Reserve Governor Jerome Powell at AEA annual meeting
11:15 a.m. Minneapolis Fed President Neel Kashkari at AEA