This decision may affect more than 100 death-row inmates.
By a 5-4 vote, the justices overturned a ruling that had applied the Supreme Court's decision retroactively to all pending death-penalty cases.
The high court's decision could affect at least 86 Arizona death-row inmates and about 25 others in Idaho, Montana and Nebraska, according to lawyers in the case. Those states had used judges rather than juries at sentencing.
If the 2002 ruling had been applied retroactively, it would have been up to the states to decide whether to conduct new sentencings before a jury or allow the death-row inmates to serve a sentence of life in prison instead.
The decision was a victory for Arizona and the US Justice Department, which argued the 2002 ruling should not be applied retroactively to inmates awaiting execution. A number of states supported Arizona's appeal.
In its 2002 ruling, the high court said only juries, and not judges, must consider aggravating factors and weigh them against any mitigating circumstances in deciding whether to impose a death sentence.
Justice Antonin Scalia wrote for the majority that the 2002 ruling did not announce a "watershed" rule of criminal procedure that must be applied retroactively to cases already final on direct review.
Under Supreme Court precedent, only watershed decisions must be applied retroactively to already completed cases.
The court's most liberal members - Justices John Paul Stevens, David Souter, Ruth Bader Ginsburg and Stephen Breyer - dissented.
The high court agreed to decide the issue after conflicting appellate decisions on how the 2002 decision should be applied.
The case involved an Arizona death-row inmate, Warren Summerlin, who was convicted and sentenced to death for the 1981 murder of Brenna Bailey, 36, a bill collector who came to his Phoenix apartment to check on an overdue account.