SACRAMENTO — In a landmark victory for supporters of assisted suicide, the California State Legislature on Friday gave its final approval to a bill that would allow doctors to help terminally ill people end their lives.

Four states — Oregon, Washington, Montana and Vermont — already allow physicians to prescribe life-ending medication to some patients. The California bill, which passed Friday in the State Senate by a vote of 23 to 14, will now go to Gov. Jerry Brown, who will roughly triple access to doctor-assisted suicide across the country if he signs it. Mr. Brown has given little indication of his intentions.

The California bill is modeled on the law in Oregon, with several notable changes. The California law would expire after 10 years and have to be reapproved, and doctors would have to consult in private with the patient desiring to die, as part of an effort to ensure that no one would be coerced to end his or her life — a primary concern for opponents of the law.

Leaders of the “death with dignity” movement said they hoped the passage of the California law could be a turning point.