Chrysler will receive a further $8bn in government aid, up from the $6bn the Treasury had promised it if it had successfully restructured the business by midnight.
The White House described the move as a "surgical short bankruptcy" which should last between 30 and 60 days.
President Obama said the "necessary steps" had been taken to give Chrysler "a new lease on life".
He added that he had "every hope" that Chrysler will become "stronger and more competitive" now that it had Fiat on board.
"It's a partnership that will give Chrysler a chance not only to survive, but to thrive in a global auto industry," he said.
'Hedge fund block'
The deal will need to be ratified by the bankruptcy court.
While Chrysler's main banks, holding 70% of the debt, accepted this proposal, it was rejected by hedge funds that hold a sizeable proportion of its remaining debt. Hedge funds are private investment funds that typically attract rich private investors.
Their stance in the negotiations was criticised by President Obama.
"A group of investment firms and hedge funds decided to hold out for the prospect of an unjustified taxpayer-funded bailout," he said.
"They were hoping that everybody else would make sacrifices and they would have to make none. Some demanded twice the return that other lenders were getting. I don't stand with them."
Chrysler is owned by private equity firm Cerberus Capital Management, which bought an 80.1% stake from Germany's Daimler for 7.4bn euros ($9.9bn; £6.6bn) in 2007.
Cerberus will forfeit its stake as part of the deal.
The partnership with Fiat will create the world's sixth largest carmaker.
Italy's Fiat will not have to pay anything for its share, which will give it access to the North American marketplace. It will also have the right to appoint three company directors.
In return, Chrysler will be able to take advantage of Fiat's expertise in making smaller, more fuel-efficient cars in its existing US factories.
No Chrysler plants in the US will close.
Fiat chief executive Sergio Marchionne said he would spend time meeting Chrysler employees and touring its facilities over the next few weeks.
"While our agreement must necessarily go through the US legal system for a few weeks, we will be preparing ourselves to re-emerge quickly as a reliable and competitive automaker," he said.
The Treasury will provide Chrysler with $3.3bn in working capital to support it through the Chapter 11 process.
It will also extend a $4.7bn loan to the new company, once it has emerged from bankruptcy, repayable over the next eight years.
Chrysler's financial arm - that makes loans to buyers and to dealers - will be merged into GMAC Financial Services. GMAC is the finance arm of General Motors (GM) but was bailed out by the government in December. The new GMAC will get government support.
Chrysler, the smallest of the US "Big Three" carmakers after GM and Ford, secured a $4bn loan from the US government at the start of the year, and has since gained $500m more.
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