It would give California an estimated $1.2 billion to make up for a budget deficit in the current fiscal year.
The approval came despite a state report last week which said the sale will end up costing California taxpayers $1.4 billion over 35 years.
The state plans to rent the office space back from the private owner.
Several speakers at the hearing questioned whether state officials thoroughly weighed all their options.
One proposal called for California to sell the buildings but retain ownership of the land, allowing the parcels to stay in the public trust until after the real estate market has rebounded.
The Associated Press contributed to this report.