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.
The state of California is changing the way it deals with some mentally ill prison inmates.
The California State Controller's office has completed payroll audits of two state agencies and found more than $1 million was paid to employees improperly or without authorization.
California prison officials have reached a tentative deal in a lawsuit regarding the use of force against mentally ill inmates.
A large medical prison facility in Stockton is once again accepting new admissions.