The policy sensitive two-year yield was at 0.87 percent in afternoon trading, about where it was before the release. The dollar moved slightly higher and then fluctuated, but the S&P 500 jumped about 15 points after the minutes. It closed 1.6 percent higher at 2,083.
"They put in December as a potential rate hike date, and they meant it. Dec. 16 is a very, very live date for action, and frankly, given the stellar 271,000 jobs report since the October meeting, we would be astounded if they don't raise rates finally," wrote Chris Rupkey, chief financial economist at Bank of Tokyo Mitsubishi. "The winds of change have finally come to the Fed after all these years. Rates are going up. In 2015. Bet on it."
Bank of America Merrill Lynch economists, however, said while the Fed kept the door open for a December rate hike, the FOMC was perhaps slightly more dovish than expected.
They pointed to the fact that "most" voters on the Federal Open Market Committee were not yet reasonably confident on the committee's inflation outlook. But they did note they still expect a December hike.
Read MoreStocks bounced as Fed appears to hold the course
In its minutes, the Fed said, "Most participants anticipated that, based on their assessment of the current economic situation and their outlook for economic activity, the labor market and inflation, these conditions could well be met by the time of the next meeting."
But it also added that the actual decision would depend on the implications in the economic data released between the October and December meetings. The Fed minutes noted that improvement in the labor market had slowed somewhat in recent months.
Steve Massocca, managing director at Wedbush Securities, said the Fed rate hike should not be problematic for the stock market, especially because of the slow path of rate increases promised by the central bank.
"At the end of the day we're talking about 25 basis points, 50 basis points. The Fed is not going to 2 percent for some period. My view is they want to get off zero, but I don't think they do much more than that," he said.
Massocca doesn't expect a big rally but the market could hang in. "There's just not a lot of alternatives for money. I know the Fed's going to raise rates but if you have investable dollars, where else do they go? " he said.
Read MoreFed left itself wiggle room
The bond market has been tilting more toward a December rate hike since the strong October nonfarm payrolls, which also showed a surprise pickup in wages.
"The Fed didn't have the nonfarm payrolls at this meeting, so the notion that a hawkish set of minutes was priced in resonates," said Lyngen. "It was definitely the most hawkish minutes that we've seen during this rate cycle."
Read MoreMost FOMC members see December rate hike as appropriate
John Canally, economist and market strategist at LPL Financial, said stocks may be responding to the idea that the Fed minutes repeated what the more than 30 recent central bank speakers have been saying. "It's almost like they got together in October and decided what they were going to say. It removes the uncertainty of when they're going to raise rates but it also moves the Fed back to the market, which is risk on," he said.
Canally said the market also takes comfort in the fact the the Fed emphasized it will raise rates very slowly.
Some stock traders pinned the post-Fed rally on short covering and the fact that the central bank wasn't really certain it would raise rates.
"I read it the other way. They've been talking through it. This reinforces what they've been saying. Unless there's a big freeze up in financial conditions, if there's not another large-scale terrorist attack or some exogenous hit that slows down growth, I don't think they wait," said Canally.