Interest rates fell and stocks went flying after the Fed's post meeting statement gave the market just about everything it wanted.

The Fed left interest rates unchanged, as expected, and suggested that it would be flexible on its balance sheet strategy. The Fed also acknowledged changes in markets and financial conditions were serious enough for it to be patient about further interest rate hikes.

Fed funds futures were showing just a 10 percent chance of a single rate hike in 2019 after the Fed's 2 p.m. ET statement, down from 20 percent earlier in the day, according to BMO. Bond yields fell, and stocks popped, with the Dow rising 434 points to end the day at 25,014.

Strategists said the Fed statement was very dovish, even more so than expected, and Fed Chairman Jerome Powell was also dovish during a post-statement press briefing.

"The case for raising rates has weakened somewhat," Powell said.

Some economists had been expecting the Fed to include a reference to a 'patient' approach to raising interest rates, since inflation is low and there is no reason to rush. But the Fed not only added that but also eliminated language from its statement saying that more rate hikes would be warranted, in "further gradual increases."

"They gave us everything and then some. On the dovish wish list, this was the best you could get. This is pretty darn dovish," said George Goncalves, head of fixed income strategy at Nomura. "Part of what I'm wondering now is are people starting to think, 'what do they know that we don't know?'"

Ben Jeffrey, rate strategist at BMO, said the Fed suggested in the statement there could be more risks to the economy by removing the phrase that risks were 'balanced. "That would be consistent with their pivot to a more accommodative stance," he said.

The January meeting follows weeks of Fed officials stressing that the Fed would be flexible and listen to the economy and markets. Powell, himself, had rattled markets in December when he said Fed balance sheet policy was on "autopilot," when markets believed it was potentially decreasing market liquidity.

""It doesn't change the message too much, but it's consistent with what they've been saying since their December meeting — that they'll be patient. They don't commit to any further rate hikes in the near term. They say they're going to be patient. It's all in context of data dependence," said Tom Simons, money market economist at Jefferies. "It doesn't say they're done by any means. It says they're going to be patient before they raise interest rates. It's more dovish than hawkish. But it doesn't signal a shift in stance."

Fed watchers had expected Powell to mention the balance sheet in his press briefing, but the Fed surprised the market with a separate statement on it instead.

"The news, which was sort of implied beforehand, is that they would stop the normalization of their balance sheet" if there was an economic reason to do so, said Luke Tilley, chief economist at Wilmington Trust. "It's important that this is something that's always been there but has been in the background, and not something they stressed...There is a change here in that they are willing to use the balance sheet as monetary policy tool."

The yield closely reflects Fed policy. The 2-year yield fell to 2.54 percent after the statement, from 2.58 percent. The 10-year yield fell to 2.70 from 2.72 percent.

Traders had been hoping to hear some more details from Powell on the Fed's program to unwind the balance sheet.

During the briefing, Powell said the balance sheet policy was under review and there was no decision yet on the size or make up of it. The balance sheet ballooned to more than $4.5 trillion, as the Fed bought Treasury and mortgage securities to provide liquidity and help the economy heal after the financial crisis through its quantitative easing program.

Fed officials have described the process to reverse it as something that would run in the background automatically, almost like watching 'paint dry.'

"Of course it's a change. They acknowledge that it has been tightening," said Goncalves. "QT [quantitative tightening] really does exist. The whole 'paint dry' concept or whatever that was is now out the window."