(Reuters) - Florida's governor signed legislation on Monday tightening state law to require a unanimous recommendation by a jury before judges can impose the death penalty.

The law is the state's latest effort to restart its death penalty process, which was put on hold twice last year after rulings by the U.S. Supreme Court and the Florida Supreme Court in separate cases.

"The law establishes clear statutory standards for how the death penalty can be applied in Florida," said Robert Dunham, executive director of the Death Penalty Information Center.

The statute, signed by Republican Governor Rick Scott, makes Florida the latest U.S. state to require death penalties to be imposed only after a unanimous recommendation by a jury. Only Alabama still allows a judge to impose capital punishment without the unanimous agreement of a jury, Dunham said.

The measure was passed quickly by the state's Republican-controlled legislature after the Florida Supreme Court in October struck down a previous law that allowed judges to impose the death penalty if 10 jurors recommended it.

In January 2016, the U.S. Supreme Court struck down a still earlier Florida law, saying it unconstitutionally let judges determine the facts that would lead to a death sentence, rather than juries. That law also allowed judges to override a jury's recommendation or impose the death penalty if a majority of jurors recommended it.

Executions in Florida, home to the nation's second-largest death row, have been on hold since the U.S. Supreme Court's ruling.

There are 382 people in Florida prisons who have been sentenced to die. Since the process of appealing death penalty verdicts can take decades, some have been on death row since the 1970s.

The only state with more people on death row than Florida is California, where 749 inmates have been condemned to die. California has not executed anyone since 2006.

It was not immediately clear when Florida would resume executions. Many of the cases in the state remain under review. The new law, along with a Florida Supreme Court ruling earlier this year, may lead courts to resume the process of deciding whether to impose the death penalty in new cases going forward.

(Reporting by Sharon Bernstein in Sacramento, Calif.; Editing by Peter Cooney)