All but four of 19 major U.S. banks got a green light Tuesday from the Federal Reserve to boost their dividends and take other steps that will make their stocks more attractive to investors. The Fed declared them strong enough to survive a downturn worse than the Great Recession.

The Fed’s findings signaled its confidence that the financial system, which nearly collapsed 3 years ago, is healthy again.

J.P. Morgan, Wells Fargo and other large bank holding companies that passed the Fed’s so-called stress tests raised their dividends and announced plans to buy more of their stock. The news ignited a late-day rally on Wall Street. The Dow Jones industrial average shot up 218 points to its highest close since the end of 2007.

“It’s clearly good news _ the U.S. banking system can now withstand a quite severe recession without falling over,” said Douglas Elliott, a fellow at the Brookings Institution, a non-partisan policy think tank.

One notable exception was Citigroup, America’s third-largest bank. It was among the companies the Fed said lacked enough capital to withstand another severe economic and financial crisis. Its stock price fell 4 percent in after-hours trading. The Fed announced the results after markets had closed.

The other three financial institutions that did not pass the Fed’s hypothetical stress test were Ally Financial, SunTrust and MetLife.

The Fed reviewed the balance sheets of 19 bank holding companies to determine whether they could withstand a severe crisis: unemployment at 13 percent, stock prices falling 60 percent over two years and home prices plunging 21 percent from today’s levels.

The overall financial system is much stronger than it was in 2009. In the first quarter of that year, the 19 companies stress-tested by the Fed held $420 billion in cash and assets easily convertible to cash. That figure climbed to $759 billion by the end of 2011.

The banks that passed the test Tuesday celebrated with announcements of increased dividends and plans to buy back their own shares:

_ JPMorgan Chase is increasing its dividend to 30 cents per share from 25 cents and plans to buy back $15 billion of its stock by the first quarter of 2013. The company’s outstanding stock is currently worth $136.7 billion.

_ U.S. Bancorp said it will boost its annual dividend by 56 percent to 78 cents per share and buy back up to 100 million shares of its stock.

_ Wells Fargo said it will increase its dividend to 22 cents per share from 12 cents.

For those banks that failed, the Fed can stop them from paying stock dividends or buying back their own stock. The Fed can also force them to raise money by selling additional stock or issuing debt.

After last year’s stress tests, the Fed allowed some banks _ including JPMorgan Chase and Wells Fargo _ to raise their dividends because they were deemed healthier.

The Fed has conducted the stress tests each year since 2009. The Fed did not publicize the results of its tests in 2010 or 2011.

The Fed released the results two days earlier than planned after JPMorgan sent out a press release late Tuesday saying it had passed the test.

After the first round of tests, in 2009, the Fed ordered 10 banks to raise a total of $75 billion. Bank of America alone was told to raise $34 billion.

This time, the Fed didn’t order any of the banks that failed its test to raise specific sums. However, it won’t allow them to increase dividends or buy back shares, and it told them to submit plans within 30 days outlining how they plan to get stronger.

Citi said in a statement that it plans to keep paying out its quarterly dividend of 1 cent a share.

Insurance company MetLife said it was “deeply disappointed” with the Fed’s findings. It had previously announced plans to free itself from the Fed’s oversight by selling off its bank division.

Ally Financial, the former GMAC Bank, was the worst performing bank in the Fed’s test. The U.S. Treasury still owns 74 percent of the bank. Ally protested the Fed’s stress tests, saying that the analysis overstated the potential mortgage risk in its portfolios.

This year’s test was more rigorous, the Fed said, so it could be assured that the industry was prepared to meet more stringent international banking rules that go into effect in 2013. The Fed said it also looked more closely at hypothetical loan losses from credit cards and mortgages.

The Fed wants banks to show they could not only withstand the crisis but keep lending to Americans and businesses.