WASHINGTON — The Supreme Court found Florida’s unique system of imposing a death sentence unconstitutional on Tuesday, saying it gives power to judges that is rightfully reserved for juries.

The decision united the court’s liberals and conservatives, who voted 8 to 1 against the system employed by a state that’s among the leaders in imposing capital punishment. Florida has nearly 400 inmates on death row.

Justice Sonia Sotomayor said Florida’s process reduces the jury’s role to an advisory one and leaves the work of finding the special circumstances that render a murderer eligible for the death penalty up to a judge.

That is the reverse of what the court in 2002 said was required, she wrote.

The Constitution means for ‘‘a jury, not a judge, to find each fact necessary to impose a sentence of death,’’ Sotomayor wrote. ‘‘A jury’s mere recommendation is not enough.’’

Justice Samuel A. Alito Jr. was the lone dissenter.

It seems likely that the ruling will have limited impact outside of Florida, because no other state has exactly the same procedure.

Sotomayor acknowledged that the Supreme Court had twice upheld Florida’s death penalty process. But the court’s ruling Tuesday overturned those decisions and said they did not square with the court’s more recent rulings.

The Florida case was brought by Timothy Lee Hurst, who was convicted of the 1998 murder of Cynthia Lee Harrison, his co-worker at a Popeyes fast-food restaurant in Pensacola.

As in other places, Florida requires a jury in the sentencing phase of a trial to consider aggravating circumstances that would make a defendant eligible for the death penalty — in Hurst’s case, that the crime was committed during a robbery, and that it was particularly ‘‘heinous, atrocious, or cruel’’ — along with mitigating circumstances, such as a defendant’s low IQ or childhood abuse.

But the state does not require the jury to be unanimous in recommending death. In Hurst’s case, the jury recommended death on a vote of 7 to 5, citing the two aggravating circumstances. But it is unclear whether all seven agreed on both, or, for example, whether four agreed on one and three on the other.

The Florida jury was also told that its recommendation was not binding and that it was up to the judge to make a final decision. And the judge could consider evidence that the jury did not.

The decision to sentence Hurst to death must be based ‘‘on a jury’s verdict, not a judge’s fact-finding,’’ Sotomayor wrote. ‘‘Florida’s sentencing scheme, which required the judge alone to find the existence of an aggravating circumstance, is therefore unconstitutional.’’