Lawmakers approved AB966 by Democratic Assemblyman Rob Bonta of Alameda on a 45-26 vote Monday.
Unlike the previous legislation, which spelled out a plan for California prisons to distribute condoms, the latest version would ask the California Department of Corrections to write its own plan.
Brown rejected last year's legislation, saying the corrections department already allows family visitors to bring condoms for overnight visits.
Bonta says a community group has volunteered to donate the condoms and dispensers. Condoms are not legally available in most prisons because it is illegal for inmates to have sex with each other.
According to the State Auditor, the average suicide rate at California-run prisons is significantly higher than the national average for other state-run prisons.
California prisons are testing a new rule for lifers.
Programs to train California state prison inmates with marketable job skills for life on the outside are expanding starting this month.
A study has found mixed results from the $15 million California spent to thwart prison drug smuggling by increasingly creative inmates.