More than four years after the worst financial collapse in a lifetime, the lingering effects that have been holding back the U.S. economy are finally fading away.

That, at least, is what investors in the stock market seem to be thinking these days as they push the Dow Jones Industrial Average to ever-new heights.

The latest evidence to support that renewed confidence came from a report Wednesday showing solid job gains in February, based on monthly data collected by payroll processor ADP.

Employers added nearly 200,000 jobs last month after hiring 215,000 new workers in January, a revision that boosted that month's pace of hiring by 23,000 more than ADP initially reported. The report suggests that the government's February jobs report, due Friday, may beat economists' forecasts of about 150,000 jobs added last month.

Those forecasters are also expecting the government to report that the unemployment rate dipped to 7.8 percent from 7.9 percent in January.

"It feels like underlying job growth continues to improve and the current pace should be enough to bring down the unemployment rate," said Mark Zandi, Moody's Analytics chief economist. "The economy is not in full swing but we're moving in the right direction steadily by surely."

After more than three years of a wobbly recovery, the emerging confidence that the U.S. economy is healing has put stock market investors in a buying mood. So far this year, the Standard and Poor's 500 index is up by 10 percent, extending a rally that has sent stocks 20 percent higher since last June.

Though job growth is still weak by historical standards this far into a recovery, the gains are broad-based, according to the ADP figures. Small businesses—which had been all but sitting out the recovery in hiring—have also begun adding to payrolls.

(Read More: 6% Unemployment Rate Still 3 Years Away—Bernanke)

The pickup in hiring in February has also returned to the housing industry, which had been all but left for dead after the worst collapse since the Great Depression. Though the pace of homebuilding is still far below peak levels during the 2000s boom, the industry has begun getting back on its feet. That recovery is expected to continue this year—some analysts expect it to accelerate.

And after nearly two years of uncertainty about the potential damage to the economy from large federal budget deficits and the ongoing budget battle in Washington, a clearer picture is beginning to emerge.

"We have to deal with Medicare and Medicaid, these are ticking time bombs," said Nariman Behravesh, chief economist at IHS Global Insight. "The guys in Washington punted on all of that, but we're not done with this. The good news is in terms of getting the deficit and debt levels down, we are making progress."