Assembly members voted 44-36 to replace the death sentence with life in prison without parole. The state Senate approved the bill Monday.
Corzine, a Democrat, has said he will sign the bill within a week.
The measure would spare eight men on the state's death row, including the sex offender whose crimes sparked Megan's Law.
A special state commission found in January that the death penalty was a more expensive sentence than life in prison, hasn't deterred murder and risks killing an innocent person.
"It's time New Jersey got out of the execution business," Democratic Assemblyman Wilfredo Caraballo said. "Capital punishment is costly, discriminatory, immoral and barbaric. We're a better state than one that puts people to death."
Among the death row inmates who would be spared is Jesse Timmendequas, a sex offender convicted of murdering 7-year-old Megan Kanka in 1994. That case sparked a Megan's Law, which requires law enforcement agencies to notify the public about convicted sex offenders living in their communities.
Senate Republicans had sought to retain the death penalty for those who murder law enforcement officials, rape and murder children, and terrorists, but the Senate rejected the idea.
Democrats control the state Legislature.
The nation has executed 1,099 people since the U.S. Supreme Court reauthorized the death penalty in 1976. In 1999, 98 people were executed, the most since 1976; last year 53 people were executed, the lowest since 1996.
Iowa and West Virginia halted executions in 1965. Other states have considered abolishing the death penalty recently, but none has advanced as far as New Jersey. According to the Washington-based Death Penalty Information Center, 37 states have the death penalty.
Bills to abolish the death penalty were recently approved by a Colorado House committee, the Montana Senate and the New Mexico House. But none of those bills has advanced.
The nation's last execution was Sept. 25 in Texas. Since then, executions have been delayed pending a U.S. Supreme Court decision on whether execution through lethal injection violates the constitutional ban on cruel and unusual punishment.
