Behind closed doors, mediators led by another judge have been meeting with Orr's team and creditors for weeks to explore possible settlements.
Rhodes has told the city to come up with a plan by March 1 to exit bankruptcy. Orr has said he would like to have one ready weeks earlier.
The city is so desperate for money that it may consider auctioning off masterpieces from the Detroit Institute of Arts and selling a water department that serves much of southeastern Michigan.
"We need to recognize that this decision is a call to action," Gov. Rick Snyder, who supported the bankruptcy filing, said Tuesday. "We are confronting fiscal realities that have been ignored for too long."
Minutes after the ruling, a union lawyer said she would appeal. City officials got "absolutely everything" in Rhodes' decision, she told reporters.
"It's a huge loss for the city of Detroit," said Sharon Levine, an attorney for the American Federation of State, County and Municipal Employees, which represents half of city workers.
Orr, a bankruptcy expert, was appointed in March under a Michigan law that allows a governor to send a manager to distressed cities, townships or school districts. A manager has extraordinary powers to reshape local finances without interference from elected officials. By July, Orr and Snyder decided bankruptcy was Detroit's best option.
Detroit, a manufacturing hub that offered well-paying blue-collar jobs, peaked at 1.8 million residents in 1950 but has lost more than a million people since then. With more square mileage than Manhattan, Boston and San Francisco combined, the city does not have enough tax revenue to reliably cover pensions, retiree health insurance and buckets of debt sold to keep the budget afloat.
Donors have written checks for new police cars and ambulances. A new agency has been created to revive tens of thousands of streetlights that are dim or simply broken after years of vandalism and mismanagement.
Former hospital executive Mike Duggan takes over as mayor in January, the third mayor since Kwame Kilpatrick quit in a scandal in 2008 and the first white mayor in largely black Detroit since the 1970s.
Orr is in charge at least through next fall, although he's expected to give Duggan more of a role at city hall than the current mayor, Dave Bing, who has little influence in daily operations.
Associated Press Writer Corey Williams contributed to this story.
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