NEW YORK—A federal bankruptcy judge in New York has approved the sale of most Chrysler L.L.C. assets to Italian automaker Fiat S.p.A., moving Chrysler one step closer to exiting bankruptcy and implementing a plan to shave billions in cash contributions to a retiree health care trust.

As the Chrysler asset sale was approved late Sunday, General Motors Corp. filed for bankruptcy protection Monday. The financially ailing automaker also wants to put in place a plan that would slash cash contributions to fund retiree health care benefits.

If it emerges from bankruptcy, which is now considered virtually certain, Chrysler can put into place a recent agreement with the United Auto Workers union. That agreement modifies a 2007 contract that had called for Auburn Hills, Mich.-based Chrysler to contribute $8.8 billion, including $7.1 billion in cash, to a voluntary employees’ beneficiary association—administered by the UAW—to provide health care coverage to current and future UAW-represented retirees. In turn, Chrysler would have had no future obligation to provide retiree health care coverage.

The latest agreement reduced Chrysler’s cash contribution—payable in escalating amounts between 2010 and 2023—to $4.6 billion, while the VEBA would receive a 55% ownership in Chrysler in the form of stock after Chrysler emerges from bankruptcy.

The agreement the UAW reached with GM also calls for a significant reduction in GM’s cash contribution to a retiree health care VEBA administered by the UAW in exchange for, among other things, the VEBA receiving a 17.5% ownership in GM after the Detroit-based company emerges from bankruptcy.

In forging the agreements, observers say the UAW is betting the VEBAs eventually will be able to sell the automakers’ shares at a price that will enable the VEBAs to replenish their cash reserves that will be depleted quickly by the health care claims they will have to pay for during the next few years.

Additionally, the agreements GM and Chrysler reached with the UAW call for the companies to eliminate, effective July 1, dental and vision care coverage for retired UAW members.