A federal appeals court in New York had earlier approved the sale, but gave opponents until Monday afternoon to try to get the Supreme Court to intervene.
Justice Ruth Bader Ginsburg ordered a temporary delay just before a 4 p.m. deadline on Monday.
Now the court has freed the automakers to complete their deal.
The opponents include a trio of Indiana pension plans, consumer groups and individuals with product-related lawsuits.
The court issued a brief, unsigned opinion explaining its action. To obtain a delay, or stay, someone must show that at least four of the nine justices find that the issue raised is serious enough to warrant hearing a full appeal and that a majority of the court will conclude the lower court decision was wrong.
"The applicants have not carried that burden," the court said.
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